I don't you need permits but I'd check with your local government commission. I'd call your insurance provider get a little liability just cover yourself if they break a window or something. You don't have to have a business license to get insurance. It's a good way to teach your sons the value of money. Show them what the fuel cost, mowers ect.
I run a larger LCO and we'll actually jump over and help young kids if they mowing next to us trying to make an extra buck. Usually just string trim or blow off sidewalks with our equipment. I think it's great seeing younger generations out trying to make their own money.