@KarlaO22 Games use a lot of battery. Even when your laptop's lid is closed, the computer is still running and still has the game fully loaded and ready to play. The processor and graphics card both draw much more power when running a game than when idle or just juggling a few browser windows, and while the draw would be less with the laptop lid closed, it would still be higher than normal. This is not specific to Sims 4 but would likely be true of almost any game.
Also, batteries wear down. It sounds like yours doesn't have enough capacity to make it through the night anymore, at least not with the game still open. That doesn't mean the battery is bad, just that it's not new.
By the way, I would never leave a game running overnight, whether I used sleep mode or closed the laptop lid. Even under ideal circumstances, it's going to hurt performance, and it can cause crashes or lag or introduce other errors that I'd rather not have to address. If loading times are long, it's easy enough to start the process and then check email or have a cup of tea or something.