Garen

PTA Runes
Pretty simple to counter Garen. The only real way he can get onto you if you are able to maintain good positioning is by using Q and flashing to close the gap. Without flash, he will never be able to actually get into melee range against you because of vayne's kiting power. You usually won't even need to use condemn defensively. Be careful though, because if he does get into melee range, he will win the trade unless you can condemn him away instantly.
Try to freeze wave in the middle of the lane or closer to your tower because enemy jungle ganks are still very deadly with garen.

Darius

Summary - PTA FOR DAMAGE, GLACIAL FOR KITING(YOUR CHOICE). MAINTAIN AA DISTANCE, PLAY AGGRESSIVE EARLY LEVELS, PLAY CLOSE TO WALLS, DODGE HIS Q, TRY TO KEEP WAVE MIDDLE OF LANE, KEEP WATCH FOR ENEMY JUNGLER.
Despite the fact most Darius players run Ghost and that Darius's kit seems like it would **** up your kiting, it's actually very easy to kite and disengage from him as a Vayne. The goal of this matchup is constantly keeping full AA range against a Darius as his pull range is 535 while your AA range is 550. When his pull is down is when you want to go aggressive and try to apply damage on him. Levels 1, you want to just last hit minions and poke darius when he goes for it, or push slightly, then get it to slow push to you(if he started pull for whatever reason and pulls you in, immediately try to disengage and back off and just last hit). Levels 2 you might still be able to keep this up depending on what he takes next, but levels 3 and on you need to be especially focused on keeping distance from him because if he pulls you in and you don't have condemn up, you are ****ed. In the case that he does pull you in, just try to tumble away as fast as possible. If he uses Q after his pull, condemn him away as fast as possible. In this matchup, its preferable to try to keep the lane in the middle or on your side so you have an easier time poking him down or even killing him. However its still okay to push him into his tower. If he has both ghost and phase rush however, you should play the lane closer to your tower or he'll be able to just flash on you, pop ghost and use his whole combo while getting movement speeds much higher than you can kite out even with using condemn.

Sett

Summary - PTA IF CONFIDENT, GLACIAL IF NOT. PLAYS OUT SIMILAR TO DARIUS, MAINTAIN AA DISTANCE, AVOID GETTING PULLED, KITE PROPERLY IF HE RUNS AT YOU. PLAY AGGRESSIVE BUT PRIO FARM. PLAY ANYWHERE IN LANE.
Matchup plays very similarily to Darius, except he has a bit better time with gap closing.
His E is pretty similar to Darius except its shorter range aka you can avoid it easier. You SHOULD be able to outkite his Q speed, and when fighting him, dodge his megapunch W at ALL COSTS! His ultimate is what allows hold you down easier. You should be taking mainly short trade, 1 full W proc, and back off to avoid his W. This is how you should be playing the entire laning phase. You can attempt to All-in him whenever you think you can pop him, but when you do so, make sure to avoid his W or at least just avoid the true damage area part of it or he WILL be able to turn the fight. And whenever he manages to get his ulti onto you, disengage as fast as possible because he will win in melee range.

Aatrox

Camille

PTA or Glacial
Pure skill matchup. Being a ranged champion top lane, you are stronger than Camille level 1 and maybe even level 2 depending on what she takes. Levels 3 and on you need to be careful because her W will out damage you unless you fully proc your W on her in retaliation, and if you get hit by her hookshot, you instantly lose the trade(and maybe even die). Level 6 you will be able to have an easier time kiting her out especially with Vayne's Ulti, and if she ults you, your condemn can knock her out of her own ring, cancelling her ultimate.
I would suggest playing this one closer to your turret so you have an easier time escaping, and would suggest just farming it out(at least until you get Botrk). Try to avoid getting hit by her W sweet spot and you MUST DODGE her hookshot.

Cho'Gath

PTA Runes
There's actually nothing he can do to you in the laning phase other then try to throw abilities at you. Granted, if you don't dodge his abilities(especially his Q) he can actually put the hurt on you, however considering its pretty simple to dodge his Q especially with your own, he's not much of a threat. Just be careful when Cho hits 6 because he can somewhat nuke you if he hits you with his Q.

Cassiopeia

Dr. Mundo

PTA Runes
Easy to counter him as long as you don't constantly eat his Q's.
Simply maintain good distance from him and kite well and try to play around minions.
Set wave around middle or close to your side.

Fiora

Summary - SKILL MATCHUP IN FAVOR OF FIORA EARLY, YOU LATER. PTA IF CONFIDENT, GLACIAL IF NOT. MAINTAIN GOOD AA DISTANCE, MAKE HER WHIFF HER Q THEN PUNISH. DODGE HER RIPOSTE, TRY TO SAVE CONDEMN FOR WHEN HER RIPOSTE DOWN PLAY AROUND WALLS, KEEP WAVE CLOSER TO YOUR TOWER EARLY. YOU START TO HARD WIN WITH BOTRK IF EVEN.
How this matchup goes is very dependent on the skill level of the Fiora. If she's good, your best bet is to try to freeze close to tower for a quick escape and to just farm it out as much as possible. Thankfully once you complete your BotrK, kiting her becomes nowhere as hard and you are able to start hard winning against her. The first thing you should do once the minions crash into each other is to push slightly into fiora and get the wave in a position to start slow pushing into your tower so you can set a freeze. Levels 1 and 2 is where you can kinda poke fiora. Just a couple auto's here and there but your priority at the moment is farming up to get your first item. Once you have the wave positioned on your side of the lane, you should focus on farm and start focusing on maintaining your distance from Fiora. If you do so and fiora tries to start a trade with you via her Q depending on how close she is to you, all you need to do is either just step back slightly or just tumble slightly back to disengage. If she straight up whiffs her Q, start kiting her out and engage on her back.(3-4 autos preferably) If fiora uses her Riposte to parry your W proc from going off, you now have a decent window of time where you can be slightly more aggressive in your pokes. If not then its free damage. Also play around walls for an easier time to stun her for better damage(just be careful when her Riposte is up). Rinse and repeat. Once you at the very least get Bilgewater Cutlass and some good attackspeed, you can start actually shoving out and playing aggressively, in which when you do, you still should kite her out properly and make sure to try to dodge her W, or at least disengage if hit by it.

Gangplank

Gnar

Heimerdinger

Illaoi

Irelia

Jax

Jayce

Kayle

Kennen

Kled

Malphite

Maokai

Mordekaiser

Nasus

Summary - PTA. RUN CLEANSE IF YOU WANT. PLAY AGGRESSIVE EARLY ON. SHOVE INTO TOWER THEN LET IT SLOW PUSH TO YOU. DON'T CONSTANTLY EAT HIS E'S. FREEZE NEAR YOUR TOWER AND FORCE HIM TO PUT HIMSELF IN DANGER TO FARM. MAINTAIN DISTANCE CONSTANTLY

Olaf

Ornn

Pantheon

Poppy

Quinn

Renekton

Summary - PTA IF CONFIDENT, GLACIAL IF OTHERWISE. PLAY SLIGHTLY AGGRESSIVE EARLY LEVELS, PLAY BACK AND FARM PREFERABLY UNDER TOWER LATER. KEEP MORE THAN AA DISTANCE AWAY FROM RENEKTON. DON'T TRY TO POKE UNLESS HE HAS NO RAGE. ONLY HARD COMMIT TO W PROC IF HE WHIFFS SECOND DASH TO TRY TO GET TO YOU. FARM AS MUCH AS POSSIBLE.
This is a dangerous matchup because a Renekton with at least 75% rage bar and just a tiamat+ignite alone can 100 to 0 burst you down in 1 single trade if you step too close to him and he knows how to combo his abilities properly. The way to go about with this match up is that, at level 1, you need to get the wave to start slowpushing to you so you can get the wave close to your side. Do this by taking down the first wave melee minions by constantly AA them then only last hit from there until the wave slowpushes to where you want. During this time, for levels 1-4, you can try to also apply some quick poke onto him. Once you get the wave where you want, you should focus mainly on farming and keeping out of his engage range. If you can get him to whiff his engage however, you are free to punish him and hard commit to a full W proc or 2. Once you get BotrK you are able to now fight him and even win IF you can avoid him locking you down with his W stun and thus busting the rest of his damage on you in that time(aka when he whiffs his dash or when its down).

Rengar

Summary - GLACIAL IS MUST. YOU STRAIGHT UP DON'T WIN THIS MATCHUP IF THE RENGAR IS GOOD. KEEP WAVE CLOSE TO TOWER, DON'T GREED FOR CS, FARM AS MUCH AS POSSIBLE, WAIT FOR JUNGLE TO FIGHT.

Riven

Summary - GLACIAL RUNES. PLAY POKE AND SET FREEZE LEVEL 1 AND 2, PLAY COMPLETELY DEFENSIVE AND FOR FARM 3 AND ON UNTIL BOTRK IS BOUGHT. MAINTAIN DISTANCE FROM RIVEN A LITTLE OVER AA DISTANCE PREFERABLY. TUMBLE BACK ONCE SHE USES HER FIRST TWO QS TO TRY TO GET TO YOU. PUNISH IF SHE WHIFFS HER GAP CLOSES. YOU WIN FIGHTS WITH BOTRK IF YOU CAN KITE HER OUT.
The Riven matchup is a skill matchup that's in her favor early on, but if you have good kiting skills and know how to play around Riven's kit, becomes completely one-sided the moment you have botrk. Levels 1 and 2, your focus is to try to set a hard freeze on your side of the lane so its easier for you to farm. You can send a couple pokes at riven if you want, but its not as effective considering you don't have PTA this matchup. The reason why we go glacial this match is because all of riven's movement abilities are affected by slows, in the same way Kalista's passive jump gets slowed. Once Riven hits level 3, your goal is to just farm and hit your first item powerspike with BotrK. At this stage, you play like a *****. You don't try to attack her and just farm. The only moment when you can retaliate against her is when she fails to gap close onto you, in which you can safely trade with her. To make her have a harder time getting onto you, its recommended to try to stay a little over your AA distance against her or at the very least your full AA distance. If done properly, riven will need her first 2 Q's to get close enough to hit you with her E dash into Q knockup. If she start's Q'ing to you, start moving back, and when she is about to use her 3rd Q or her E dash, tumble backwards to make her miss it and you'll have free damage on her. Even more so with glacial helping you catch up to her(note, use only 2-5 auto's depending on how close you are to her.) Once you get enough gold to get your BotrK, you can hard win full all-ins with her as long as you can kite her out. It's recommended to start all-ins by baiting her to try to rush at you, aka staying closer distance to riven, and when she is getting close enough to start her wombo against you, use R into immediate tumble to the side or behind her and kite her out.

Rumble

Ryze

Shen

Singed

Sion

Swain

Sylas

Tahm Kench

Teemo

PTA Runes
His threat is dependent on how good he is. If he's a good teemo player, you hard lose this match and most likely get put far behind. If he's not so good however, you can actually win against him in a straight out all-in if he uses his Q for poke rather than defending against your all-ins.
Overall however, play close to tower and try to farm it out.

Trundle

Tryndamere

Urgot

Volibear

PTA Runes
Plays similarly to garen but with a bit less damage, and a slightly easier time locking you down.
His Q duration is much longer than garen's own Q speed up, but you still should be able to outkite him.
The reason why he's a lower threat level than Garen however is because while he can get close to you easier, he doesn't have as much damage output as garen and with good kiting, you should be able to kill him.
Play middle of the lane preferably

Wukong

Summary - EVEN LANE PRE 6, HE HARD WINS AFTER 6. TRY TO GET A FREEZE NEAR YOUR TOWER LEVELS 1-5 AND FOCUS ON FARM. KEEP DISTANCE FROM HIM. IF HE TRIES TO DASH TO YOU, IMMEDIATELY TUMBLE BACK AND YOU CAN START KITING. LEVELS 6 AND ON PLAY CLOSE TO TOWER AND JUST FARM IT OUT. DON'T ENGAGE ON HIM. JUST PLAY FOR MID/LATE AND TEAMFIGHTING.

Yasuo

Yorick

Summary - RUN PTA. FARM LANE MAINLY. DON'T GET HIT BY HIS MIST, TRY TO KEEP HIM FROM STACKING TOO MUCH GHOULS, DON'T GET LOCKED IN CAGE, PLAY SLIGHTLY AGGRESSIVE EARLY LEVELS, PLAY PREFERABLY BY TOWER. ENGAGE ONLY WHEN HIS MIST TOSS IS DOWN.
The Yorick matchup is a bit tricky to pull off at first but once you get it down, its really easy to play against him as he is actually really immobile. First thing to note is knowing how he normally trades, being amassing a bunch of ghouls, hitting someone with his E, then kiting away from them with his W. So the way to play this is start playing semi-aggressive early on, just an AA or two here and there, and keeping the wave in the middle or nearer to your tower. Once yorick hits level 3, he should have all his abilities and thats when you should watch for when he has 3 graves set up and MAKE SURE TO DODGE HIS E. If you do get hit by it, at least don't get caught in the cage or you will lose a large chunk of your hp. If he starts putting his W around you, a quick tumble movement should be able to get you out before it fully forms. Your goal should still be to get the wave frozen on your side of the wave and then farm. However in this matchup, you are able to go for full trades ONLY after Yorick misses his E on you. It's also a good idea to take down ghouls when you can as they can mess up the position of the lane quite a bit. Starting level 6, you need to be a bit more careful. Play the same way but if he uses his ultimate, immediately back off or else you will lose trades you take against him due to the auto target function of his ultimate. When his ultimate is up, try to find occasions to try to whittle the maiden down until it fully goes down. You start to win full all-ins with botrk as usual.

Vladimir