It depends on what the contract says.
And anyone who leases out their horse (that has any monetary value that they would be that upset about) and does not require the person leasing the horse to carry Equine Mortality insurance with the owner as beneficiary is not too bright.
If there is no contract and it was a simple lease then I can not see the person leasing owing the horse owner anything.
OK, now I re-read the OP and you are asking if the horse owner owes the person leasing anything? The person leasing paid the lease ahead? Or the person leasing wants to be paid back for something else?