The best champions out of lane to counter Evelynn include Draven, Caitlyn, and Lucian. These picks are all good at countering Evelynn with win rates over 55%. Even if these Evelynn counter picks are not chosen in your lane, it's not a good idea to play her into any of these matchups. They will very likely destroy Evelynn.
Conversely, if the enemy team picks either Olaf or Amumu, you should strongly consider taking her, as she easily crushes these champions with win rates over 51% against both ofthem.