Has anyone done any home maintenance on the mower? The most common cause of lean mixture in Hondas that I know of, is a split gasket on the insulator that goes between the carburetor flange and the intake port. If the carburetor mounting nuts have never been removed, though (same nuts that hold the air filter body), the gasket will be all right, and the only other prospective cause is a blocked jet or (perhaps more likely) emulsifier tube. The emulsifier tube is directly above the jet. You can unscrew the jet with a screwdriver, and it will drop out, followed by the emulsifier. Clean out all the holes, and remember to put the emulsifier back in the right way up (flange at the bottom: you'll see the rub mark where the top of the jet has pressed against it).