Hi! This is just my own build to Lux. Now the reason why I dont put anything after archangel's is I don't think its necessary. I usually win the game a couple minutes after my archangels.

I'll just make a small list of pros and cons here..

Pros

Fun (In my opinion at least)
Super charged laser of death
Easy to use

Cons

A tad squishy
If your spells are on cooldown you are useless

Doran's Ring
Health Potion
Boots of Speed
Amplifying Tone
Ionian Boots
Mejai's Soulstealer
Rabadon's Hat
Archangel's Staff

After this you can pick a varity of items such as .. another archangel's, deathfire grasp, rod of ages, zhonya's hourglass

Alrighttt skills!!

Light Binding - Your snare! Just like Morgana's snare. Remember to take into account the enemy's movement!

Lucent Singularity - Your AOE slow and damaging skill! Press E again to detonate the ball of light. When in team fights leave the ball until they are about to get out of ball range.

Finales Funkeln - Your ultimate! It has a small delay, but it wont cause any missing problems. The delay isn't enough for the enemy to escape the line where the laser will strike. Rather easy to aim!