vaybe is seriously broken, and riots community have been complaining about her since the stone age of LOL.
She does so much damage with lethal tempo and the three aformentioned items (grieves, botrk, rageblade) that you dont really need to build more damage, and people who do, go 12/5/4 instead where if you build like me, you will go 22/1/8.

the main reason is people think they need to build more damage on her, but you really dont. Vayne being a short range dps champion relies heavily on being in the middle of a fight. where instead of building more attack speed, she should be building HP items armour and resists, or gaining utility items such as slows from iceborn gauntlet, or building experiemental hexplate to reduce her ultimate cooldown resulting in being invisible more often in fights. once you start building heartsteel and jak'sho earlier on vayne, you will see a large different in your ability to close out games. if you start building her like this, you will notice a sharp decline in the number of enemy champions being able to single you out. Meaning, if they dont have an answer for tank vayne, then what can they realistically do?
make sure to check out the notes ive made in the item section for more information on build paths in different senarios.

So for build path, straight-forward, build the magical three items i keep refering to. Get boots first, then vampiric sceptor for sustain in lane.

Vayne is a punching bag in the early game, she lacks items to proc lethal tempo in early trades, and she has no abilities to trade well with early on. She is super item reliant in this way making her a walking, typing minion on the rift early on. but the game wouldnt be fun if she could go 5/0/0 in the first five minutes then build 2 items, then tank up and walk through the enemy every game. We have to make it hard for her to hit her item spikes, simply because she is that broken.

Her only poke ability is her Q tumble empowered attack. Which is very strong when executed properly. always Q towards an enemy just as theyre about to last hit a minion, AA them and run back. when timed correctly, they will have no opportunity to retaliate, and continue to do this until they are low, then run them down with your passive, or better yet once you've hit lvl 6.
vayne has one of the biggest lvl6 power spikes in the game, where she can go invisible, dodging everything with her reduced tumble cooldown, increased movement towards enemies, and an attack damage buff that pretty well gives her an item advantage in the form of stats. So be sure to abuse this.

Vayne is great in low elo, because in pro play, she is shut down easily in the early levels due to her potential in carrying the game. But in low elo, nobody respects this damage potential she has.

If youve never played vayne, your first week of playing her will be devastating. you will go 0/10/0 for the first 12 games. most people dont make it past this first week of horrendous feeding because vayne initially makes you feel like youre bad at the game. But trust me, shes one of the hardest champs to play in the game even though her kit os so deceivingly simple.
so to answer the question in this heading;Why vayne so bad in low elo? Because she is hard to pilot. And people who think they can vayne top get crushed 90% of the time because you have to have such an incredible understanding of her match ups and have perfect positioning all of the time. But if you think you micro is solid, and you know how to kite like a pro, vayne will carry you out of a lot of low elo dumpster fire games. I recomend watching saskiolol on youtube how to play her, he will have a lot of advice. Though use my item builds, because, face it, until youve played vayne for years, you will need tank items to compensate your lack of perfection that saskio has achieved.

avoid inistiating fights with vayne, especially earlier on, shes too squishy man. but after 4-5 items, i will play really aggressively, within reason (there does not exist a champion who can 1v5 with zero map aeareness yet, and once the is, im giving up playing forever).
vayne will often want to hit the person in fron of her, she is excellent at destroying the enemy front line with her W passive. you will sometimes find great opportunities to attack the back line, but careful not to over exdend yourself in fights, especially before getting a sustain item.

does your team suck too much? have they fed too hard, where you guys lose every objective?
try split pushing, it is a subject you should research, and i wont get into it here. though for vayne, she is a very strong split pusher. i would only buy hull breaker after a wave clear item, and only if team fights are 0% winnable. you will want to focus on buying movement speed items to escape being colapsed on. because, if your team is feeding, you can expect to be the only one over extended on the map while your teammates are hiding behind whats left of your towers, or worst aleeady dead.

items like ghost blade, dead mans plate, stride breaker, and triforce will be your friends here