This problem requires some critical thought and the process starts with heat. What does heat do to an engine? It makes the fuel hot if the gas tank is located near the engine and it heats up the ignition system. It also affects the choke system if it is not adjusted properly. Heat expands things and this expansion affects the metal tolerances inside an engine.
You may use your mower for 15 or 30 minutes and then shut it down to remove a stick from the yard or refill it with fresh gasoline. You pull the rope or turn the key and nothing…nada.
First, let’s check the choke to be sure it is working like it should. Is it closing and opening normally? If not, this could be the problem.
Second, let’s check for spark and see if you have a good blue spark if you are using the plug to the cylinder head method. An inline spark tester will show a bright orange glow or a bright blue spark depending on the type of tester you have. On occasion once an engine is shutdown and heat soak has begun, it could affect the sparkplug or the ignition coil and not allow good spark to occur.
Third, are the intake and exhaust valves properly adjusted to the specs your engine calls for? Valves that are too tight or too loose will make for a no start when hot.
Lastly, you may have water in your fuel that is making it hard to start. Take a fuel sample at the carburetor to see if you have any water in the fuel or other contaminants.
By checking each one of these items one by one, you can home in on the lawn mower will not start when hot issue.