It is not uncommon for your lawn mower engine oil to smell like gas. If you have a leaky carburetor needle and seat, the gasoline will seep past it and overflow the carburetor and end up in the cylinder. Once inside the cylinder, it will seep past the piston rings and end up in the crankcase.
What causes this is a buildup of deposits on the needle and seat inside the carburetor. These deposits cause the seal to not work properly and the weight of the fuel pushing on the needle will overcome it and then allow fuel to go past it.
Two things will need to be done to resolve this problem.
The first thing is to completely clean the carburetor. It must be disassembled and cleaned entirely.
The next thing is that the oil must be changed. Warm the engine up for a brief time and then remove the oil and replace it with the proper oil. Synthetic oil is fine to use in your lawn mower engine.
After you have run the engine and changed the oil. Fill the gas tank up and check the oil the next time before you mow to see if you smell any gas or if the oil level is higher than normal. If everything is OK, you should be fine to use your lawn mower.