This whole idea of asking for/giving a refund if a horse goes lame during a lease is pretty new to me, and pretty ridiculous IMO. The entire purpose of leasing a horse, whether full or part leasing, is to get to ride a horse that you might not otherwise be able to afford, plus get experience with horses outside of just taking lessons. This means that you should be expected to help with all aspects of horse ownership.
Poor management from the owner causing lameness? End the lease.
Serious injury that will have horse out for more than a month (that didn’t happen under your care)? End the lease.
Horse acted like a horse in the paddock and has a scrape or tweaked fetlock or what ever else? That’s part of the life of owning horses. If you’re unwilling to accept such risks when leasing, then don’t lease, certainly don’t buy, and stick to taking lessons.