Lux insane range and cc spells should let her not getting in the way of dying early on, and because of that, I have decided to focus only high damage items early on. With some skill and a bt luck mejai should have some stack quite early, without you dying. After that comes high ap rabadosn and the synergizing Lich bane. To be really succesful with Lux, and not like those coward "i dont want to die" luxes that run around and leave u and your team behind everytime, her passive+lichbane is must to learn. If it were possible I even wanted to have some Crit, and really punish with those pewpew autoattacks. But the 2% from masterie is the the top, because Magicpenetraion is much more important.
After that in my build, comes the flexibality, and like all mages items shall be replaced with what u need. Here I gotten in one RoA for the allroundness and archangel for staying power.
But ofc, a void staff agaisnt tanks is a must, and sometimes an Zhonyas hourglass can be real nice to have agaisnt like Xin, Karthus, poppy or like. The only problem with this build is the lack of cd. I rely on Mejais, and blue potions and Blue runes and the bit of masteries, and maybe the blue golem buff.