I hate to ask, but did you get permits? Every garage I've done that had a room below it, all the engineering and waterproofing were detailed out in the plans. It's normally 4" of concrete over the plywood subfloor sloped towards the door. Sometimes additional sheets of plywood are stacked in the back if the joists can't take the extra weight of the concrete. One hour fire protection in the walls and basement below too since you have living space around it.
If you told the building department you were going to store a mower in there, they should classify it as a type U occupancy. They'd want to see all the details that apply to fire protection and waterproofing in the plans that correlate with a Utility occupancy type. That's why it seems strange you're asking these questions now.
You can call your local building supply and ask what they offer for outdoor waterproofed decks and balconies. But even if you got the best stuff on the market, I don't know how well it would work in this application, or how safe it would be. What if his mower leaked gas? Then it spills onto a wood deck with no slope? And with no fire protection between that and the living space?
