The best picks globally to counter Lux include Jinx, Caitlyn, and Aphelios. These champions are all good at countering Lux with win rates over 54%. Even if these Lux counter picks are not chosen in the same position as you, it's not smart to choose her into any of these matchups. They will very likely destroy Lux.
Conversely, if the opposite team choses either Singed or Karthus, Lux mains should strongly consider choosing her, as she easily beats these selections with win rates over 52% against both ofthem.