Thank you so much for the explanation and your solution !!

This happens pretty much to everyone in the vanilla game because of the unusually high scores on the leaderboards obtained by obvious cheaters that the game can't handle for some reason, hence the crashes. Thankfully, there IS a way to disable the leaderboards by using mods, like Fusion Fix: https://github.com/ThirteenAG/MaxPayne3.FusionFix . Tried and tested it personally and it works like a charm: no more crashes when entering co-op lobbies.

How did you make this mode work ? For me it crash every time no matter online, private or lan game...

Had a blast playing this.