most probably a simple fuel starvation caused by dirt or old fuel in the carb.
-for carbs with float bowls (honda, tecumseh, some briggs, some mountfields) -remove the carb, remove the bowl/float+needle/main jet, blast the whole lot with carb cleaner and if possible finish with a blast of compressed air over all the carb parts and the carb itself including through all the openings in the carb, then reassemble.
-for briggs classic with the tank top plastic carb, you need to replace the carb diaphragm.
this should get ya going again.
this problem is usually caused by dirt blocking the main jet on carbs with floats and bowls. or caused by an old worn or baggy carb diaphragm on the briggs.
could also be an air leak, you can test this by starting the mower (only do this test from cold) then spray carb cleaner all around the carb and where it meets the engine, if it runs correctly then you have an air leak and need to renew the gaskets between the carb and engine.
Andy Lee, June 2009
