Is your mower doing just fine on a hot day and then suddenly it dies? Does it die all of a sudden and then will restart after a while? Does it seem to run fine on a cooler day?
These are symptoms that point to a bad ignition coil. An ignition coil provides the spark to the spark plug that provides the ignition to the air and fuel mix in the cylinder. If you lose that spark, then the engine will immediately die and will not restart.
Ignition coils are known to break down when they get hot. The internal windings can form a break in the wire and as the temperature grows inside the coil, the wire can separate and cause the spark to stop. As the ignition coil cools down, the wire will reattach itself and then the lawn mower engine will start up once again. It tricks you into thinking that there is some other problem with the lawn mower that is causing it to die. You start searching the fuel system in most cases to try to find out what the problem is.
By checking the ignition system first, you will avoid troubleshooting the entire engine and find your results quicker.