The greatest picks globally to counter Illaoi include Kalista, Zeri, and Samira. These are all good at countering Illaoi with decent win rates over 53%. Even if these Illaoi counter picks are not chosen opposite your position, it's not smart to choose her into any of these matchups. They will most often destroy Illaoi.
Yet, if the enemy team picks either Skarner or Heimerdinger, Illaoi mains should seriously think about taking her, as she easily dominates these selections with win rates over 54% against both ofthem.