When I wrote one, the biggest thing was who was liable for what. Any injuries, to you or the horse, needs to be stated in great detail.
Also, cost of lease should be accounted for in the agreement, so that the owner can't change it on you at any moment without a decent reason. Also, account for what you are responsible for to pay for the care of this horse? Just a flat rate to the owner, or shoeing and board? These need to be specified.
And then a written agreement on when and how it should go for termination of lease, or changes in the agreement.
I have found that though lease agreements are a lot of work, they are very necessary. Being through protects not only you, but the owner also.
Get everything in writing, and have it witnessed by an uninvolved, third party.
Determine who is responsible for regular maintenance costs and who is responsible for less common things such as emergency vet calls. For instance, your lease horse needs his teeth floated; who pays for that? Farrier, deworming, coggins, and shots are generally at the expense of the person leasing the animal, as they come due on a regular basis.