I have an LT180 with about 500 hours. It started cutting out while mowing, after it got hot, maybe 15-30 minutes. Just like you turned the key off. However, I knew it wasn't a spark problem, because I could pull the choke out when it was cutting out, and it would take off again for a bit. Ah ha, it had to be a gas problem.
I put all new fuel lines from the tank forward. I took off the fuel pickup line and used the opposite end, for a fresh connection, and I put a new fuel filter and fuel pump. This didn't cure it. I still am getting a lot of bubbles coming into the fuel filter. Maybe I need better hose clamps, or a new fuel tank pickup tube.
Cleaning the Carb: I took the carb apart the first time and cleaned it. That didn't cure it. The 2nd time, I took it apart further. There is a side brass screw on the top half of the carb that needed removed to help clean apparently. I also broke off the pilot needle's (low speed jet) limiter so I could take it out and clean it's orifice. I used Auto Zone's house carb cleaner. Don't get it on you, and wear safety glasses if you use it. It's potent. I also inspected the carbs needle valve under a microscope. It had a concentric ring, where it sealed into the mating hole. But I believe it was working OK. I also routed the fuel line with fuel filter to a more horizontal position where as, the fuel filter was almost vertical. (not sure it had anything to do with this).
Lastly, my plastic hood broke off one of the pegs that it hinges on. I went ahead and took the hood off. It ran fine yesterday, for whatever reason.
BTW, my RIO switch's rubber accordian protector shield has about had it. I don't want to disable anything, as I now have my 15 yo daughter on it, and teaching my 10 yo son to drive it.