I think the new owner has to honor whatever your contract was with the old owner...so no, it's not your responsibility. Just curious, but do you think the other tenant--the woman--also is being pushed to mow the lawn? My guess is no. But I guess the question is--can you live with a nasty looking lawn and if not, is it worth your while to work out some kind of arrangement: you'll mow the lawn once every two weeks if they supply the lawn mower and offer you some kind of compensation ($$ off your monthly rent). Of course, you'd still have to haul the lawn mower in and out of the basement. Could you talk to the new owner and simply ask if they've hired a service to take care of lawn maintenance?