Don't use Lucent Singularity (E skill) on the first level, and try not to waste mana in general. Always basic attack your enemy after snaring him (Q skill - Light Binding) to activate the passive. Use Your pots after dropping below 100 mana. Don't go B if You only need mana, because it's important to get Your ulti as soon as possible so You can get a kill. Try to get the blue buff whenever possible.

Don't forget that it snares two targets on it's way not one, so You can still snare a champion who is behind a creep.

Even though I don't get this skill until I've maxed out the others, it's extremely important and many people under-use it. It isn't that helpful in early game because that's when damage output scales larger to the shield size, but later on in the game, after You've accumulated a lot of AP stay close to Your allies because You can save their a$$, especially if there is a Karthus in the enemy team. When he starts channeling his ulti try to shield all the allies around You. You can run away from the boomerang to extend it's range. Also notify the others that You can shield them.
It's cool to use the shield when helping only yourself to run away, it appears instantly on You right after You cast it.

Don't forget that You can activate it's effect if You press E after casting it. Try to predict the way Your enemy's champion will move after he notices the pattern and tries to run away from the circle (even though it's pretty hard to run away from it as it slows You down and if You activate it instantly). It has a huge range so if Your ulti is on CD You can use it to last hit enemies. You can also use it to steal kills but don't do that :P

Using it as Clairvoyance

If You cast this spell in the grass You can see enemy champions there so if You're not low on mana and You see someone missing in top/bot lane, use 'E' to check the grass before going deeper towards the enemy tower.

Get it only if You're getting kills and not dying, if it's not going good, get Deathfire Grasp instead. Even if You get it and You're not getting enough stacks, don't be afraid to sell it.

Try to remember how much damage Your ulti deals and try to use it only when You would get a kill. Also, don't waste it when You're sure someone is gonna die without it. Don't be kill-greedy. In lategame Your ulti should do 1200-1400 dmg so it could kill someone on half of their HP so don't only look at the HP bar but the actual numbers. Also, when You're chasing someone, remember that the effect is a little bit more than the range circle it displays while targeting, so fire the laser in the moment when the one You're chasing has entered Your range.

I rarely die with Lux even when I am not getting kills, because every spell besides her ulti that she has helps her get away. When someone is chasing You first snare them, then cast E where You're standing, which will slow them down (no need to activate it unless You can get a kill), and if You need it, activate Ghost. Use flash only when You need an instant getaway card, or when You're jumping walls.

I really like doing this, and in my opinion it's a good idea, however there's a lot of people who judge me for it. The idea is to stand above Baron's pool while the other team is killing him, when he's on low HP cast the E skill around Nashor and press E again to activate it when You see it will kill him. If You're skilled enough You will steal Nashor and get the buff for Your team even though the other team did 99% of the job. :)