I am on my second lease this year and although it was difficult to let go of the first lease, the barn that horse was at was just too far away and there were some other reasons I chose to end the lease (absolutely nothing to do with the horse or his owner! I just couldn't see myself being at that barn any longer and owner was not going to move the horse elsewhere for my lease).
My current lease, there are many aspects of him that remind me so much of my old gelding that I had to give up when I was 20 years old. It really is uncanny! And i'm boarding him at the same barn I kept my old gelding at for many years too. It is like coming back home. I hug my lease horse, and tell him I love him (which I do, but horses are darn easy to love, eh? Lol), and I truly feel he is a good match for me in the now, but I also know he is not the horse to take me where I want to go someday, he is not my 'perfect horse', and he belongs to somebody else. I'm borrowing him and I know one day I will be giving him back to his owner. Keeping all that I just typed in the forefront of my mind helps a lot! I am attached to my lease horse, but attached for today and yesterday more than tomorrow.
I think what would help you when you lease out your horse, is to have a set time frame for the lease. That way both you and the person leasing know exactly when the lease starts and ends, and then both parties can plan around that. For instance, my lease is on 6 month terms. At the end of January (end of the first 6 months), I decide if I want to continue leasing this gelding or if I want to hand him back to his owner. I think it's a good time frame, 6 months allows somebody to get to know your horse well, and decide if they get on well enough with them for longer leasing past the initial 6 months.