Need help - Cub Cadet 1862 dies after running

[Coyote machine]

Regarding fuel lines; older fuel lines were NOT designed to run Ethanol gas and can collapse on the inside of the line, restricting fuel flow to zero. So if you have old lines replacing all of them with fuel line designed to handle Ethanol is a good baseline to cover that potential issue. And making sure there is no actual physical restriction of flow from the cap on down to the engine at each location, at the exit from the tank, etc. forward to the entry to the carb.
You will not solve the problem until you isolate it to fuel or electrical. So far, I'm hearing fuel delivery issues....