I start off with a meki pendant to allow lux maximum laning time. As soon as you have enough, you can get a tear of the goddess or a soulstealer if you are doing well enough. Rod of ages is all the health you will need because lux is meant to be in the back of all team fights. Max out your AP late game with archangels and a rabadon. Lich bane can be bought earlier. Sometimes shen is most useful during the laning phase because your autoattacks are safer to attempt while laning

The tear of goddess removes the need for clarity, and flash is much more important anyways. Flash can be use to get out of sticky situations where as clarity is useless with an archangels because of the already massive mana regen the archangel gives.