The top picks not in lane to counter Kha'Zix include Kalista, Zeri, and Caitlyn. These champs are all good at countering Kha'Zix with high win rates over 57%. Even if these Kha'Zix counter picks are not taken in your lane, it's not smart to take him into any of these matchups. They will most often destroy Kha'Zix.
Conversely, if the enemy team picks either Karthus or Naafiri, Kha'Zix mains should strongly consider picking him, as he easily dominates these selections with win rates over 52% against each ofthem.