The best champs out of lane to counter Irelia include Karthus, Kalista, and Caitlyn. These picks are all good at countering Irelia with decent win rates over 56%. Even if these Irelia counter picks are not chosen in your lane, it's not smart to take her into these matchups. They will likely beat Irelia.
Yet, if the enemy team picks either Leona or Skarner, you should strongly consider taking her, as she easily dominates these champs with win rates over 55% against both ofthem.