The game requires Google Play Services for the pedometer to work (the game uses the new Recording API to count your steps while the game is closed). On GrapheneOS I’ve heard it works if you run it in a sandbox. You don’t need a Google account for the Recording API to work, and according to the developer documentation data is stored locally.

If you can run sandboxed apps woth Google Play Services, it should work, but I’ve not heard from LineageOS users any experiences.