When a lawn mowers engine is blowing out white smoke from the exhaust it's caused by the engine burning oil.
It could simply be caused by the tipping over of the push mower to clean the blades or check the blade or cleaning the grass from underneath the push mower.
Sometimes people will tip the lawn mower over on it's side which then allows oil to get into the carburetor which then leads to the intake where the engine then burns off that oil.
If the engine stops blowing the white smoke after awhile then that's likely the cause but if not it could mean that the piston rings are worn out on the lawn mowers engine causing the oil to get into the lawn mower engines cylinders which is then burned off when it's running.
If it's the piston rings then it's costly to fix and wouldn't be worth fixing the piston rings but most times it's just because oil got into the engines intake through the carburetor and it clears up after awhile.
But just be sure to check the engine oil level because if oil left the engine and got into the carburetor then your engine oil level will be low.
Another cause of white smoke from a lawn mower is a blown head gasket which is pretty cheap to replace and easy or it can also be moisture in the fuel but your engine would run rough if the moisture was in the fuel.