League of Legends (LoL) Question: Full AP damage?

If you're just looking for a good place to start on how to build Lux, Schroedha's guide looks pretty good to me, at a glance.

There are a few things to consider on Lux.

Runes: The big ones here are Magic Penetration Marks, and flat Ability Power Quints. Some people take defense for Seals and Glyphs, some people take some cooldown reduction for Glyphs, and some people go full greed, and get scaling ability power. That choice is up to you.

Masteries:
For most burst mages, you'll want 12 ferocity and 18 cunning, taking:
Sorcery
Fresh Blood or Feast
Natural Talent
Double Edged Sword or Bounty Hunter
and
Savagery
Assassin or Secret Stash
Merciless
Dangerous Game
Precision
Thunderlord's Decree

For items, you'll want to open with a Doran's Ring, and maybe get Dark Seal.
If you need more mana sustain, Morellonomicon is your bet, as it gives you decent damage and DPS scaling via CDR.
Otherwise, you can build straight to Luden's Tempest for early burst damage, and Sorcerer's Shoes, or Rabadon's Deathcap and Sorcerer's Shoes. If you 10-stack Dark Seal, upgrade it to Mejai's Soulstealer. If not, sell it later.
From here, Void Staff is the only other really big damage item you'll need. Everything else is utility.
Liandry's Torment is a good late game item for bursting squishy targets on Lux, due to the flat Magic Penetration.

Hope this helps at least a little!
Note: For the highest damage possible, you'll have to look into items like Seraph's Embrace, but I don't recommend this in a practical sense, as the build path and ramp-up on it are terrible on Lux.

Morelonomicon -> Luden's Echo -> Rabadon's Deathcap -> Abyssal Scepter -> Void Staff