I would guess that most of the time you are just out of luck. That is probably something you should go over with the person you are leasing from. I know that my barn offers leases on the lesson horses, but the way they do it is, if the horse you are usually riding for the lease becomes lame or otherwise unridable, they let you ride another lesson horse for the remainder of your lease. Now obviously if you are leasing from someone with just the one horse, this isn't an option. So again, you would have to talk to the person you would be leasing from.