This is a very common problem. You keep pulling the pull cord until it finally starts or you turn the key and crank and crank until it finally starts. Both result in the same hard starting lawn mower engine.
It comes down to a common few things that cause this problem. One is you are not getting enough fuel in the engine because the fuel pump is going out or there is an obstruction in the line, fuel filter or the carburetor. Try turning the engine over on a riding lawn mower with the fuel line disconnected at the fuel pump outlet line and have a catch can waiting to catch any fuel that comes out. If fuel comes out readily, then your fuel pump is fine.
On a gravity fed system. unhook the fuel line at the carburetor and see if fuel comes out. You will need a tool to pinch the fuel line closed and they make a special one with smooth jaws for this. If you don’t have a way to stop the fuel from flowing, you will have a big mess to clean up!
If fuel is going to the carburetor, then pull the spark plugs and make sure they looks slightly wet with fuel. If they are, the problem is most likely your valves are out of adjustment.
On a push or self-propelled lawn mower, to test for fuel getting to the engine, pull the cord or turn the key on an electric start a few times and then remove the spark plug and see if there is fuel on it. If there is, your valves are probably out of adjustment if it is an overhead valve engine.
Another common item to cause this problem is the choke not set properly or it is malfunctioning. Check to be sure it is closed when you are starting the engine and slowly opening as the engine warms up.
Blown headgaskets can also cause hard starting and low cylinder pressures due to bad piston rings or valves that are not seating well. The carburetor may not be venting either and throwing a lot of fuel into the engine flooding it. The needle and seat may be failing an flooding the engine as well.
Bad fuel or water in the fuel can also cause hard starting in your lawn mower.
Check each system one at a time to help narrow down what the problem is and then find out which specific component is the culprit to solve my lawn mower is hard to start problem.