How do you get the PROJECT: Pyke Mission Icon?
It was a mission or event reward. Riot's description in the client reads: “This icon was rewarded for completing the final PROJECT Pyke mission during the 2019 PROJECT event.”
Is the PROJECT: Pyke Mission Icon still available?
No. Riot tied the PROJECT: Pyke Mission Icon to 2019 (mission reward), and it does not normally bring back past event rewards or bundles.
