Mejai's is not a Core Item...

why do you put 2 points in fury and waste 2 points in auto-attack minion damage when right next to it you can get 5% cdr? Lux needs to get to 40$ cdr the fastest she can and those 4 points are well used.

I'm not quite sure why you guys are so afraid of Mejai's Soulstealer. It's a beast of an item, and unless you're dying repeatedly because your team isn't peeling for you and you're positioning poorly (which you shouldn't be), then you don't lose stacks all that quickly. The item is 100% gold efficient at only 5 stacks, and it's 355% gold efficient at max stacks.

Max stacks on Mejai's Soulstealer isn't all that hard to get, especially considering that all of your spells are AoE which means you can score multiple assists quite easily. Normally, I wouldn't recommend Mejai's Soulstealer as a core item on an AP caster, but due to Lux's range and AoE potential, I see no reason not to pick it up.

Also, Athene's Unholy Grail + Morellonomicon is an amazing item combination that essentially replaces your dependency on blue buff. You'll be able to stay in the field much longer, and the reduced damage from not taking a hard AP route isn't even that bad.

Doran's Ring is also a geat start option even more the better start option. Bulding both Athene's Unholy Grail + Morellonomicon isn't necessary but I think it's more importan to skip Mejai's Soulstealer. Magic Resist Runes are possible too and Greater Mark of Hybrid Penetration seems to work nicely with her passive.

Armor Seals are correct, Mana regen Seals are situational. She will take damage at laning phase though as you know, trading with the enemy.

Also. armor seals? Shouldn't it be either MR or mana regen? i doubt lux needs that armor at all, she is a mage which simply means she won't and shouldn't be played to take damage, thus rendering the armor seals unnecessary. recommend mana regen seals.

Zhonya's Hourglass > Mejai's Soulstealer. One good assassins simply shuts you down, alongside your mejai stacks. You need the durability, or else you are simply too fragile and all. Your build has no defense in it, any bad positioning is a goner for you.

Mejai's Soulstealer is not a core item. You should take either Athene's Unholy Grail or Morellonomicon, not both.

Mejai's Soulstealer is a situational item, you only get it if you are snowballing very hard.