Once you land your Q on someone squishy, press E>R>E in quick succession. This should 100 to 0 most AD carries, once you get your Deathcap and Void Staff.

Your first buy is a bit tricky. These are all assuming you have around 1500 gold.

Usually, you'll get a Chalice, Fiendish Codex and Boots on your first back. Follow standard core.

The first alternative is to grab an Armgaurd and another Doran's, if you're up against an AD laner. This gives you the armor you need to survive lane. Switch Zhonya's with Deathcap on the standard build.

Another option is to get a Tear and a Forbidden Idol. This is mostly for farm-heavy laners like Veigar, Malzahar and Anivia. You want to be able to shove them harder than they shove you, and ultimately out-damage them come late-game. This build path leads into the alternative core item slot, and will give you moar AP by the end game. Grab a Negatron Cloak ASAP after the first back, as anyone you build this against will burst your squishy *** down. Eventually, you want to turn the Negatron into an Abyssal or a Quick-Silver Sash, but just hang onto it until after your Archangel's.

A final path is to rush a Mejai's. I recommend this only to those with yoloswag, as it is not for the meek. Build the standard core items afterwards.

The problem that most Lux players run into after finishing their core build is, "What do I get next?". This obviously doesn't apply if you rush a Mejai's, but with the standard Athene's rush, it's a moderate issue to consider.

Lich Bane, Twin Shadows, Rylai's Crystal Scepter, Liandary's Torment and Abyssal Scepter are the optimal items. Feel free to grab DFG or Banner of Command, if you're feeling bored.

Get Mercurial Scimitar if you hate being suppressed. It kinda sucks.

Lich Bane, while encouraging risky, greedy play, allows for a whopping ~750 damage auto-proc (calculated from 600 AP) when combined with her passive. Oh, and you get bonus MS.

Twin Shadows's active makes it easier to see and hit targets, while providing MS and CDR. This is good, and can get you to the max 40% CDR, but since you'll be getting the Blue Elixer and/or Blue Buff at that point in the game anyway, you don't really need this stat. The 80 AP it gives is decent, so I'd still consider buying it, but Rylai's grants 100 AP, in addition to a heavier slow and 400 HP. Granted, it doesn't provide vision, but still.

Liandary's Torment is good against tanks, since it does 2% HP, and gives flat Magic Penetration. This one also gives HP but slightly less than Rylai's (300 HP).

I do not recommend getting Mejai's Soulstealer as your 6th item, since it takes a while to stack up, and only becomes gold efficient at 5 stacks. Optimal stackage is around 10. Caveat Emptor.

Don't get Gaurdian Angel - if the enemy team kills you once, they'll certainly kill you again, and the item provides no AP to give you a stronger shield. It's just not worth buying unless you're some slippery, unkillable hypercarry like Master Yi, Udyr, Katarina or Poopy.

I'll put this in list form, for the sake of organization.

Get boots and a second Doran's Ring before your Chalice of Harmony if you're against Ahri or Xerath. You need the MS to evade their skillshots.

If not against either of those champions, get boots after Chalice.

Upgrade boots after your Athene's Unholy Grail, and before you get your Needlessly Large Rod

If you have enough gold to get a Rabadon's Deathcap straight out of the shop, but haven't upgraded boots yet, don't upgrade boots. The Deathcap is more valuable.

Always upgrade boots before your Void Staff.

Enchant your boots whenever you have enough gold left over, after your Deathcap is finished.

I know this list isn't complete, but I don't have the time to finish it. Let me know if you want me to add any specific matchup.