The best picks not in lane to counter Lulu include Kalista, Zeri, and Karthus. These champs are all good at countering Lulu with win rates over 58%. Even if these Lulu counter picks are not picked in the same position as you, it's not a good idea to choose her into any of these matchups. They will often beat Lulu.
Conversely, if the opposing team choses either Skarner or Ziggs, you should seriously think about taking her, as she easily wins against these champions with win rates over 51% against both ofthem.