I need more information to give you a better and more accurate answer.
But most times if your lawn mower just started smoking at startup if it's a push lawn mower is it could be that oil got into the carburetor when it was tipped over or you put too much oil into the lawn mowers engine.
If the smoke goes away and doesn't come back then it's likely just too much oil or oil in the carburetor that needs cleaned out.
If the smoke is white then that's indicator of a blown head gasket or moisture in the fuel or any other related components.
If the smoke is white then it can be an issue with the fuel system or carburetor and the most common problem is the fuel to air mixture ratio is too rich which means that the carburetor is getting too much gasoline at one time.
A clogged air filter can cause this problem or a carburetor that needs tuned.