Has insurance been discussed? That's where things can get tricky.
We had a horse on 'trial'. Problem was, the owner had us sign a contract that if she was injured for any reason we would pay the vet bills until she had fully recovered, and if it was a permanent injury we would buy her, and she hadn't been worked in three years. This is quite common. She broke the halter within 5 minutes of leaving her house, and was pacing the trailer. That was the longest drive ever, and we live nearly 2 hours from them. Once we got her home we were too leary of her coming up lame to do anything with her, so she had a two week vacation in our pens (followed by another nerve-wracking drive home). The terms of the contract are extremely important, and absolutely make sure there will be a contract for both your sakes. If it's too strict, it can really limit the enjoyment you can get out of the lease (e.g. the risk of taking the horse to shows/clinics/trail rides elsewhere), and can come back to bite you in the butt.
Insurance is absolutely vital for both parties. We had a stud horse on loan here at the ranch a few years back. Other than getting kicked in the knees by mares, what can happen to a stud in a 10,000 acre pasture? He got struck by lightning within the week! He was stone cold dead, and it was so severe his hooves were blown off. Thankfully the owner was a friend and was understanding, but we had to give him all of that year's horse colts so that he would have another stud prospect.