I hate to sound so insensitive here as I know you are confused and upset, and rightfully so, but do you also see the humor in this...humor in a sad way? The lawn service guy? Really?
Instead of letting it send you into an emotional whirlwind of self-righteous indignation and strategically planning how to prove him wrong, could you try to laugh it off because it is just plain old ridiculous? So the guy friended you on Facebook - he is probably using FB as a way to maintain his business contacts and keep clients.
My RAH did this to me once. When I finally stopped laughing, I just felt sorry for him because it was a pathetic attempt at projecting his own BS onto me. And the man he accused me of cheating with is still a good friend and colleague who happens to be one of my work mentors.
I told my husband that day I would never, ever again participate in such a nonsensical conversation and he could take his accusations and stick them where the sun doesn't shine.