@zzzzz9200 I found this under FAQ, but it doesn't say 3 moves for both sides. . .
How do I delete a game?
If a game is under three moves it can be deleted from the 'My Games' page by clicking the bin icon. If a game is three moves or over, it can not be removed, but can be archived.
@zzzzz9200said Do we lose a game automatically if we quit before our 3rd move as black?
As long as you can delete the game it is uncounted.
If you have a tournament game (or clan or ladder) you can still resign before two full moves have been performed. Your rating is not affected, but the game is documented (at least in tournament and clan games for coherence reasons.