I agree with gertie. If you want a warmblood, expect the lease to be in the $10-15k+ per year range.
Small correction - a leasor, aka lessor, is the owner that leases out the property. Lessee is the one leasing it. Typically the lessor creates the lease agreement, not the lessee.
Depending on the value of the horse, you can expect terms such as the lessee must pay for mortality and/or major medical while leasing the horse, a “return in same or better condition” clause, lessee is responsible for all vet, farrier, and care of horse. The owner might put restrictions in such as max fence height allowed to be jumped, max number of shows per month, no one else is allowed to ride the horse without written permission.
IME, a full lease means the lessee pays all vet bills, farrier bills, etc., regardless to how the injury occurred. If you’re doing a full lease, it doesn’t matter if the horse gets injured “unrelated to riding.” The horse is in your care, and is your responsibility, and it’s unfair to expect the owner to have to pay vet bills on a horse who got injured while in your care, not theirs. It’s a wonder owners lease their horses out anymore, with the number of people that think a lease gets them off the hook for injuries/illnesses.