A fuel filter on a lawn mower can last many seasons without needing changed as long as you use clean fresh gasoline in the lawn mower then you shouldn't need to replace the fuel filter for many years.
It's best to have a fuel shut off valve in between the gas tank line and the fuel filter of the lawn mower so that when you're done mowing grass for a week or for the season you should turn the fuel shut off valve off and let the fuel filter and carburetor run completely out of gasoline.
This will keep the gasoline from gumming up in the fuel line and fuel filter and also if you plan to store the lawn mower over the winter without running make sure to run the gasoline tank dry so that the gas doesn't turn to varnish and cause problems.
I have a riding lawn mower that I've been doing the exact thing with and never had to change the fuel filter so far in the 5 years that I've had the lawn mower.