how about do without him owing you a favor
He won't owe you anything. You should do it and expect nothing in return.
Only do things for people because you want to do them. You'll be disappointed every time if you do it for any other reason.
Wrong. He never asked you to do it.
That would be very nice of you but avoid the "he'll owe me a favour" bit or you'll come off as a douch
That's not how favors work.
Why do a lot of men believe that if they do you a favor, then you owe them one too?
If you do mow it, do it because you want to give the guy a hand not because his grass is getting long and it bothers you.
NO - you will mow his lawn out of the goodness of your heart
A thank you, is enough gratitude for me.