I just worked on a buddy of mines Exmark and chased my tail around for a week. Acting like a fuel issue sometimes, or a heat issue, then maybe an electrical issue. Ended up being the kill switch on the seat. Basically, did a hero kit. Had recently done service, oil/air/fuel filter, new blades. Would run but would stop intermittently. Had to choke it to get it fired back up. So, we put a new fuel pump and cheap chinese carb from Amazon on. Still issues. Changed out the parking brake switch. Still an issue, then the seat switch and that remedied it. Really odd.
I would do the air filter first, but if that don't get it, do the fuel pump and fuel filter.