Lawn mowers can be finicky machines. They can be easy to start one day and hard to start the next. In most cases it is a simple adjustment to make them easier to start.
This adjustment is often a valve adjustment. Over time the valve clearance become loose and will not allow the valves to open properly. If the intake valve does not open fully, a fresh charge of gasoline will not make it into the combustion chamber. If the exhaust valve does not open fully, the hot gasses will not be expelled out the exhaust pipe and it prevents fresh gas from coming into the combustion chamber as well.
An engine is basically an air pump. Air goes in and air goes out. Whenever that cycle is interrupted, it makes it hard to start the engine. Try adjusting those valves to their proper specification and see if it makes a big difference in the starting of that engine.
You should also check to make sure that the choke is working properly. An engine choke is a butterfly type valve and you close in the carburetor. When it is closed, it creates more vacuum inside the carburetor and pulls more fuel through it and into the engine. If the choke is not closing fully, then fuel will not be adequate enough for a cold start operation.
By adjusting the choke and valves, you should have an easier starting lawn mower.
