Hmm. The seldom used vehicle is always the one scenario that throws all mileage based programs awry.
Usually, I would do it in 6 month intervals, regardless of oil used. In fact, I have a Dodge Ram 2500 with the Cummins diesel that I do precisely that with, as it doesn't see 5K miles/year at this point due to the fact that the fuel is over $4 per gallon these days.
That lawn mower of yours probably will keep on running like a top, as I knew of someone that NEVER changed the oil in theirs, and it lasted for 15+ years!! Good luck with getting a new mower.