When a customer comes in with a problem like yours this is the way I go about diagnosing it
1) fit a clip on volt meter to the battery leads ( old car one )
2) fit an orange in line spark tester to the spark plugs so I can see it when mowing ( 2 on twins )
3) grab a secondary fuel tank & pair of pliers.
While mowing I monitor the volt meter & spark indicators
When it dies I watch the spark testers
If they glow then as the engine starts to slow down flash and continue to do so till the engine stops then I know it has a fuel related problem ( fuel, carb or valves )
If not then I know it is an electrical / ignition problem .
The instant it stops the secondary fuel tank gets hooked up to the carb & I attempt to start the mower .
If it fires right up and runs then I know it is a fuel supply problem so will be some where from the carb inlet to the tank, including the tank vent .
Now if I can not blow back through the fuel line from the tank side of the fuel pump ( pump has check valve in it ) then I suspect collapsed fuel lines
If it is hard to blow back then goes easy I suspect a blockage inside the fuel tank near the outlet.
If the fuel line sucks back as I take it off & it is easy to blow back through I suspect the tank vent .
TO quote Hlw49, diagnosis is 95% of the job, fixing it is the easy bit .
People on forums all have "that" problem in the back of their minds which sent them mad and have a bad habit of projecting that onto others .