It would really really help if we knew what mower and which engine.
Classic example is a customer who not being used to a Honda engined mower was filling the oil to the level indicated on the dip stick, fully done up, thus the oil level was just low enough that the mower would start when cold & and all the oil was in the sump, but would not start hot when the oil was distributed around the engine and of course once it sat for an hour it would start again.
Similar with a Kawasaki engine with oil cut out that would always stop going up hills.
Another customer with a gravity fed engine was always bringing it in for service because the mower used to cut out when mowing around his dam.
Ended up being such a slope that the carb was higher than the fuel if the tank was less than 2/3 full so it simply starved.
Right now I have a Honda 4120 in that would continually backfire but not start, ended up being nothing more than a throttle cable that was rusted solid.