Is there a way to trigger something in lua when a new game is started?

IIRC: In single player I believe is a hook, but for multiplayer you're going to have to use the bout list or check for "autosave..." in the console or such.

The most realiable way is to check if get_world_state().replay_mode has changed from 1 to 0 and get_world_state().game_paused changed from 0 to 1 between two frames.