Hello,
There isn't a fuel filter in the gas tank on that model, there is a screen that covers the fuel pickup tube inside the carb.
You have a 10323 or 10324 there.
I see you're missing the primer bulb, you can fit a primer bulb off a small Tecumseh 2 stroke snowblower on your mower. It's made from rubber as opposed to the flimsy plastic Lawn-Boy used.
Magnesium decked Lawn-Boys were used on the earlier models, later ones used steel and aluminum.
Regards
Jeff