I agree with some of the comments above. I'm a fairly advanced Lux player on EUNE, and I can recall that almost all item choices are situational. However, since people started it, I'll make a list of some things I find arguable in the guide.

• When against a champion that deals heavy magic damage, your first back should be Boots and Chalice of Harmony. This allows you to defend yourself better, and sustain your mana pool in early game.
• Deathfire Grasp and Lich Bane are both very situational items. While you benefit from both of them, and they certainly are steroids, you can't use them against everyone.
• You should add Liandry's Torment as an alternative to Void Staff. Especially when the enemies are assassins and not tanks, you will benefit from the extra health. Dishing out a part of your magic penetration won't matter in this case because they won't be stacking magic resist anyway.
• It's safer to start with your CC spell, especially when you have no escapes. Whether you're protecting your jungler or invading, you will benefit more from starting with Light Binding instead of Lucent Singularity.
• Even though you're squishy, you can play safe. There's no need to use 18/12/0 or 18/8/4 masteries on a caster that benefits from all the damage she has. Use either 21/0/9 or 21/9/0 instead.
• Taking a second point on Prismatic Barrier in early has proven useful against your worst nightmares, such as Kassadin or Zed.
• You should also take a look at Summoner Spell options.
• Aside from these, I'll only leave an image from my own games :) Good work on the guide though.

Image here

I will list somethings that I think you'll need to change/add:

• greater mark of hybrid penetration > Greater Mark of Magic Penetration. This Mark synergies very well with Lux's passive, it will also let you to be able to farm more easily and you could also poke the enemies with your AA to deal some more damage.
• Mejai's Soulstealer is not a core item, its a situational item. You can buy this if only you get many kills early.
• Standard Masteries should be 21/0/9 if you are going mid lane.
• You need to add more explanations on the Runes, Masteries and Ability Sequence chapters.
• Put the Lux's abilities explanations in 1 chapters.

Good Luck ^^

Thanks, i will update ASAP

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Changed, thank you for telling me

• Greater Mark of Magic Penetration > Greater Mark of Ability Power
• Mejai's Soulstealer isn't core at all and Deathfire Grasp is viable but your core items in general against AP are Athene's Unholy Grail + Rabadon's Deathcap + Void Staff and against AD you might build Tear of the Goddess + Morellonomicon and ofc Zhonya's Hourglass.
• 21/0/9 Masteries are the way to go.