Many people, if you ask them if they want a gift, will say no just to be polite. In this scenario, if somebody said "I'd like to take care of the lawn for you if that would be helpful," I would deny the request because I wouldn't want to impose on them.

Just going ahead and doing it for me would be amazing. The number one gift anybody could give me in a tough situation is to not force me to make one more decision.

Which is to say, I guess it comes down to knowing the person.