Will kerosene damage a lawnmower

It depends on where you put the kerosene, but generally, if you just put it in the fuel tank, just drain it, put in new fuel, use some starting fluid to get it running and after fighting the pull cord forever and having it die multiple times and after putting up with the smoke while you clear out the kerosene... it will run pretty much the way it did before. The hardest part will be getting the left-over kerosene out of the engine. Understand that there is some inside the cylinder and it will take a little time to burn it out. Just get as much out as you can then start it. Kerosene is an oil and it will not harm the engine unless you try to use it in the crankcase.