A lawnmower that emits white smoke probably has an engine that is burning oil. This is most likely caused by the oil being overfilled or the engine receiving an excess of oxygen.
Lawnmower engines also burn oil when they are filled with an incorrect grade of oil. Operating a lawnmower on a steep incline may also cause oil to burn; it is better for the engine and safer for the operator to mow across the face of a hill, rather than up and down.
Any air leak, even a small one, causes a higher oil mist than the crankcase breather is capable of handling. Check for air leaks in the crankcase or leaks caused by worn cylinders or rings.