I am just setting up my fifth lease, I bought two of the horses I leased and am pretty sure I will end up buying this one too, just want to make sure we are right for her and she is right for us.
I too used a lease agreement I downloaded off the net, we lined out parts we did not like and wrote in things we wanted.
Some things you may want to add or consider:
1) my lease spelled out the location horse was to be kept at and could not be moved to a new facility without approval
2) spell out if you want them to obtain mortality insurance on the horse
3) who will pay for routine vaccines, shoeing etc AND how often those are required to be done..the third horse we leased when owner got her back from previous people leasing her she had not had shots/been wormed or trimmed.
4) spell out who can ride your horse...we wanted my immediate family including kids to be able to ride and had to sign a release.
5) spell out feed, supplements etc..can she be trailered anywhere, can she be entered into shows, gymkhana etc...
Pretty much try to spell out anything applicable so it doesn't cause problems later.
Don't take life so seriously. After all no one gets out alive.