Yes,i find Lich Bane to be a good item but there is no space.
You need all the items i listed and i would put Lich in only if you failed the Meja really hard (trust me that is ****** impossible ^^)

You probably never played Lux or you are doing it COMPLETELY wrong.
The damage you have EARLY is just sick compared to others because getting stacks of Meja on Lux is child's play! I guess that in theory this guide looks bad and expensive but please give it a try and come back. If you manage not to have Deathcap and at least 3-4 kills by 20-30 mins you are probably just a bad player or you faced Kassadin ^.^

Feel free to downvote me if you please.
But i'm not lying or anything; I play Lux since i started this game ( a year or something like that) and Rylai's Crystal Scepter is the ONLY HP item i would take. You must be thinking of RoA right? There is no space for a early Catalyst the Protector we already need Meja and Tear of the Goddess. Also the slow on you low CD Finales Funkeln is really overlooked.
btw you cant call Light Binding a reliable escape ability, Prismatic Barrier is a shield not escape ability and slow won't help you a lot when you see Warwick coming out of the brush.

Cool build bro! But why no Lich Bane ? It's so awesome at Lux because you use your AA's very much ( Illumination) Also i love the pic at the end GJ :)

Very good build,I like it :)

loving this guide :) it worked perfectly for me

nice build it's works perfect! :)

Ok you sead that Lux has no escapong skills in your cons. WTF? She has three escaping skills! Shield, stun and a slow! I wouldn't reccomend taking Mejai's or whatever... Take it only if you are shure that you can get loads of kills. Rylai's on Lux? It might be good on certan casters but on Lux? It offers so little for a caster like Lux. Not gonna vote. If I would have voted it would be a -1, but I don't -1 people. It's rude!

^above

Ridiculous that you would say there is no damage.

The build incorporates Meja's Soulstealer which i personally find to be an AMAZING item on Lux due to her high assists especially huge range on skills. If you are building the route of AP nuker, she is definitely meant to be played similar to Kassadin as a killer that comes out of nowhere and stacks on soulstealer.

My problem with this is that Ancient Tome and one red potion earlygame will offer you good damage, but be unreliable due to lack of important earlygame stats. Remember that the first items you buy can possibly last you a while into the game if your lane is successfully sustained. Also, Archangel's Staff is an item that should be built early, if at all.

I would personally suggest starting with a Doran's Ring (possible even getting two) then building a Catalyst of Aeons and turning it into a Rod of Ages and removing Archangel's Staff from the build.

please take a peek at my blitzcrank guide and vote/feedback for me (link below) thanks <3

Great guide! I used it and it works perfect! :D