Hello,
My daughter has a small push mower with a Briggs and Stratton Series 300, 148 cc engine that runs lean after the initial startup. It seems to run okay for about the first 20 seconds after startup, but then it starts running rough and behaves as if it is running out of gas. It seems to have a reasonable amount of power, but runs poorly. I have cleaned the air filter, changed the sparkplug--a long shot--blown out the gas lines the best I could, removed the cover and cleaned the "sail" on the governor. I have also tried running the mower temporarily without the air filter, but it didn't make any difference. Thank you in advance for any suggestions.
formnas

Empty the gas tank into a qt jar. Is it clear or orange colored ? Colored? Discard to roots of a bush you need to kill in the yard.

Find carb and remove float bowl - dump water and old fuel, clean bowl and reinstall and don't damage bowl seal gasket

Refill with new gas. After three times normal starting procedure and o start try Starter fluid in air intake to help restrart.

Don't work? Then you have to remove carb and do a cleaning job to remove clogged old gas that turned to varnish that clogs fuel lines. Then try again.

I pretty much agree but have a suggestion. Try adding about a 1/2 cup of SeaFoam or any good carb cleaner and then run the engine. If it runs well enough to use the mower go right ahead. Your engine is starving for fuel so its likely a clog in the carb. Dropping the bowl and flushing the bowl and needle may also help.