I looked at your Lux build. Mine, with rageblade stacks, has as much AP and more damage and attack speed. She works a lot like Ezreal - you have to hit with several spells and attacks before you can go for the kill. As you state in your build, you have to nibble with Lux. If you cast three spells in a row that means you will have three chances to hit with Lich Bane and her passive. However, her normal AS is not nearly enough to do so. With Nashors tooth, you will ignite you passive and hit with Lich Bane much faster. The whole while this is going on you are gaining more and more AP from rage blade. by the time you shoot off your ult Lich Bane will hit for 400, enough to finish them AFTER being hit every time without fail. That is why you build Nashor's tooth. More passives, lower CD, faster farming. Items like Archangel's staff don't work with her because they are made for champs with nukes, of which she only has one. not to mention that her nuke should only be used to finish off very very low HP champs or clear large minion waves very quickly.

Guinsoo's and Nashor's tooth?

I'm sorry but i dont agree with this at all. You only need to auto attack once after a spell to ignite your passive. Also her range makes it so its not difficult to hit them.

Also their isnt enough AP for Lux. Which she NEEDS. im sorry, but its a - from me.