Hey guys, I'm a Lux support main. I got mastery level 7 with her at around 30k points and currently have around a 70% winrate with her. Read my guide to learn how to consistently carry as an AP Lux support.

Start with your E and start poking. It's easy to land and hard to dodge, so make sure you spam it. Don't worry about people going into bushes, your E will reveal them. DO NOT LET SOMEONE JUST STAY STILL IN A BUSH. I've seen so many Lux players just allow enemies to hide in bushes. DON'T. Punish them by throwing out your E, which will both reveal and damage them. Don't ward bushes (just use your E) unless it's a hooking champion like Blitzcrank who loves bushes.
In fact, if you have a lead, you want to go into bushes so you can zone people with your Q (root). It's a great way to zone enemies off and make them waste a free ward on you.
Spam your E and don't worry about the mana costs, since the enemies will recall soon anyways if you poke them right. You want to buy Tear of the Goddess when you recall so you can spam abilities without running low on mana.
Once you get Q, throw it out from time to time to threaten the enemy, but don't spam this ability as it's hard to land and easy to dodge in lane, and it will just waste your mana. DON'T be scared of ganks too much because you can easily escape with your Q and E. Of course be wary if you're pushing too much, but you don't need to be that scared.
After your first recall, you want to push the wave with your ADC then go ward. Roam mid if you think they need help with a kill, and secure dragon with your jungler. Let your ADC get some solo XP during this time. Come back to lane and start harassing your opponents again.
Once both you and your ADC have ult up, you want to engage in an all-in. As long as you land your root, it should be easy to go in an all-in with both of your ults. For this reason, it's important for you to hit level six faster than your opponent.
During midgame look to take first tower with your ADC, then roam to secure objectives and help losing lanes. You are great at teamfighting, so most of the times you'll be able to take dragons and Heralds. Let your team peel for you and shield them while rooting and ulting your enemies. There's not much else to it.

Like I said earlier, just look to help any lane that needs help. With you around, you'll win around 80% of the teamfights as long as the enemy isn't super fed. Push and get towers.
As soon as you get your first mythic (most of the time Luden's Tempest), you'll hit your powerspike and your damage will start to hurt a lot. Just landing an E on a squishy will take away a third of their health. You need to abuse this by constantly throwing out your E. With your full combo, you'll be able to delete squishies nicely, so if the opportunity arises, go for an all-in.

Your late game is very strong and with 2-3 items your damage output will most likely be the highest. (Your ult is on a very low cooldown). Dish out that damage whenever you can, by this point of the game you should be able to almost kill squishies with just your Q and E. One thing to beware is that in the late game, everyone else will also have a ton of damage output, so you need to be careful of your positioning. STAY IN THE BACK, and let your team peel for you. Shield them from the back and ult from the back, since your ult range is very long.