Lux's lane phase is easy. Safe farm and poke your opponent with E + hit. Because of her passive you trade well and Q is quite nice for 2v2 fights or jungle invades. By Mid Game , your main goal is to hit a Q on a squishy and unload your full burst. Your ulti's low cooldown(20 sec with full cdr) means it will be up again when the fight starts.
Tips & Tricks
Use your E for vision in places you have none.
Try warding the enemy blue. You can steal it with your ulti when the enemy jungler tries to pass it to their mid.
Late game, don't be afraid to poke with your ulti pre-fight. Keep in mind that it's best used on enemies who can't regenerate health (like the support/ap carry)
Lux works exceptionaly well with heroes that can immobilize the opponent as they allow her to land her spells without fail.
She also synergizes with champs that can clean up well.
Lux struggles against assassins and really tanky heroes. She has a hard time getting away from assassins and lacks the sustained damage to deal with those who can survive her burst.