When playing against a Lux mid, I suggest using combos such as your root and then pop blossom. As soon as you throw your root toss your pop blossom and then immediately fall back unless you plan on making an all in for the kill. Play conservative and try and stay under tower as long as she is present in lane. If the Lux is dead, then as long as you have a minion horde of at least six then you can push up to tower as long as you are not being pressured by the jungler or someone else who is lane hopping. If you have shapesplitter upgraded to at least level 1 out of 5 then every third basic attack will do extra damage to the tower. Early game, if you do not have a plan of build with items, then i suggest leveling your shapesplitter to unlock the extra damage attack and going with attack speed to be able to attack tower quicker and do more damage in less amount of time. I find that building Nashor’s Tooth can be wonderful for attack speed AND ability power. I also suggest building magic resist, my boots are Mercury’s Treads which decreases the time on slows, stuns, roots, silences, and other CC effects. Lux’s slow and stun will be rendered useless with these boots. Playing against a Lux, you need to build magic resist and CC cancels. Once you have done this, you need to pressure lane as much as possible.