There's no way to know for sure unless I could see the engine itself to look at it.
However if you overfill the oil reservoir on your lawn mower engine it could create back pressure which can cause your engine to burn the excess oil and it would likely smoke as well.
Another reason for a lawn mowers engine to burn oil is worn piston rings that allow oil to pass through the piston into the combustion/ignition chamber portion of the engine and then it mixes with the fuel and air and gets burnt.
Exhaust valves that are warped or worn exhaust valve seats on the engine could also cause engine oil to be burnt.
If the engine is not overfilled with engine oil then it's likely due to the above engine problems I listed.