Not Updated For Current Season
Hi this is my 1st build so please go easy on me.
Simple Support/Tank Lux. You max out shield as soon as possible and try to always be there when fights start. In a fight:
1. You shield the teammate which the enemy is focusing.
2. You ensare the enemy damage dealer and hit him to activate your passive.
3. Use Ult and E to deal some damage or catch an enemy who is running.
4. Remmember you have Shurelia's Reaverie which gives 40% movement speed which can help your teammates escape!! Also you with this build you have high hp so don't be afraid to take some damage!
Choose between GA and Banshee Veil for last item depending on enemy team.
A bit weird build for her i know, but with it you can deal high amounts of damage both magic and physical...
For items it all depends on the situation but your first 4 should be sorcerer's boots, nashor's tooth, malady and hextech gunblade after that you go for madred(show those tanks that their armor & hp doesn't matter :D) and finish with GA or Banshee veil depending on whether the enemy has hard CC or not.
Main idea of the build is to have very high mobility and to be able to deal amazing amounts of damage. With nashor's tooth and elixir of briliance/golem buff you will have 40% cd reduction so you shouldn't worry about using your ult whenever you can.
P.S. I removed the AP Lux build since you can find at least 2-3 more guides for AP Lux.