here are some of the things that can cause a mower engine to run rich:
malfunctioned carb...maybe some factory mistake? maybe the main jet lost a rubber seal or even missing? there is a hidden air needle "valve"..usually located at the top of the carb, sometimes covered by a dummy welch plug. (this is rare, but sometimes the factory sets this hidden air needle "valve" incorrectly...
the choke valve might be stuck closed or will not open all the way...restricting the flow of air into the carb
the air filter is fouled, or something within the air filter box and plenum is blocking air flow.
fuel leak somewhere? look for any kind of pin hole in fuel lines, or leaking fuel line connections to the tank, fuel filter, fuel pump, carb. Especially notice the fuel line rubber grommet that connects to the tank....make sure fuel is not leaking there or from a tank leak or a loose cap where fuel sloshes up and out or evaporates when stored.
weak spark plug ...gap might be too wide...or inadequate ignition module energy..
does the oil smells like fuel? is it thin and runny? if so, it's possible that fuel is getting past the piston rings into the crank case. the piston rings need to be staggered ..they the butt ends all line up, you can have unburned fuel getting past the rings. But usually if this is excessive it will cause engine performance problems like low power...or surging.and the governor surging...excessive oil in the oil breather that reaches the air filter may be due to overfill of oil, but can also be fuel getting past the piston into the crank
valves are not lashed properly, or automatic compression release device on cam is borked. If the valves are not set correctly....even just one valve in one cylinder can cause a 4 cycle timing problem...usually this presents also as a drop in performance, misfires, surging. A leak down test for bad valve lash and worn or incorrectly installed piston rings can help identify the problems without removing the head cylinders.
and finally...