At this stage, I'd recommend heavily biasing your early build towards full Cooldown Reduction. Use that to get more chances to practice landing your skillshots. It caps at 40%, 45 with a cunning tree mastery that you're around the level to start getting.
That tip would be similar for a lot of champions. But Lux is also very happy to be spamming her kit frequently most of the game.
Mid:



I don't really support Lux much, and I don't know what support really looks like in low level games. But as an example of some 40CDR supporty builds






All of these hit the CDR cap, and have some mana related stuff built in to give you a lot of opportunities to hit spells and try to land things. You don't want to build more than 40/45CDR generally.
These builds aren't necessarily optimal for most things, and it'll definitely be different as you level, from patches and otherwise. But they'll help you learn the stuff to do with your hands, which'll be important the whole way.
Play proactively and try to use your cooldowns to get that practice, and get a feel for how much you have to hold back to not run out of mana.
As priorities, I'd try to learn to tap people with your E. You can press E while it's travelling to queue up the pop as soon as it arrives.
I'd try to learn to poke someone out with R from a screen and a half away.
I'd try to learn to catch people with Q.
As you get Q down in particular, you can start learning to combo off of it when you know you're going to hit while it's traveling. You can then get E, R, and as you speed up, an auto in as well, all off the Q landing.
Your W is buffed a good bit in almost all of the support builds I listed, but most of what you do still comes from the rest of your kit.
I'd turn on smartcast for everything in your hotkeys settings if you haven't already. You don't have to immediately if you don't want, it does help to get used to the shapes of the skills early on.
I'd unlock your screen if you haven't, especially for a champion like Lux. She's got too much range to play in locked screen.