Of course; you attached a "strange" version, without B4XPages and now you are talking about 3 B4XPages...!
Also, why do you write something like:
I try to close using the Steam Client button
do you think that makes sense to us? Is there a "Steam Client button" in B4X?
(I'm (almost) kidding).
Every time B4XPage : Game shuts down, I need it to go back to B4XPage : Lobby , but if I use the code below, the game doesn't shut down...
I can assume that you switch from B4XMainPage to the Lobby b4xpage, from this one to the Game b4xpage and when you exit from here, from the Game page, you want to go back to the Lobby, not closing the app, right?
So from the Lobby you should open the Game without removing the Lobby, i.e. using the normal ShowPage command, not ShowAndRemovePreviousPage and then you have nothing to do to return to the Lobby, just close the Game b4xpage.
If you mean that by closing the Game page the "actual game" still "runs", then probably there is something inside the Game page that you did not stop before closing that page.
Excuse me but with the information you have given (which seems more confusing to me than myself ?) and with the "surreal" projects you have attached, I am not able to help you more than that. Others will probably be able to.