The engine runs on starter fluid so this is a fuelling problem. not mechanical or ignition.
1. Clear the breather vent/hole in the fuel cap. If air can't get enter the fuel tank to replace the fuel flowing down to the carbie, it creates a vacuum in the tank strong enough to stop the fuel flow. To test if this is the problem, try running the mower with the fuel filler cap removed.
2. If it checks out, remove the fuel line at the tank end to test if fuel comes out of the tank. If good, put it back like it was
3. Then remove the fuel line at the carbie end and see If fuel is reaching the carbie end of the fuel line. If good put it back like it was.
4. If your carbie has a drain screw at the bottom of the bowl, remove it to see if fuel is getting into the bowl. If it isn't, adjust the float height. Make sure the float opens and closes and is able to move freely in the bowl. If your carbie has no drain screw, remove the float bowl. It might be easier to do this test on a bench with a remote fuel supply. While you're there, make sure all the jets are clear and that the throttle opens and closes like it should.