Usually, in full leases, the leaser will be responsible for the horse's feed, farrier and vet bills. If they are on property, then board is usually included in the cost of leasing, if off property, the leaser is also responsible for finding a place to board/keeping the horse, and arranging the horse's feed, farrier and vet.
In full leasers riders are usually looking for a cheaper alternative to owning a horse, where they can work with their horse and grow together and focus on their training. Full leases also provide all the experiences of owning a horse without the long term commitment.
It depends on a lot of things. The discipline, what level rider you are, what you want to do with the horse, the list goes on and on.
For example, if you take barrel racing lessons, (this is just an example) and you decide to want to lease a horse, you need to take into consideration what level rider you are. If you are a beginner, you may not want to lease a horse just yet, because they could have some issues that you may need to solve, but have no idea how. Some issues when leasing a horse as a beginner are that you never know what's going to happen, just like with any horse. If the horse you were leasing bucked you off, you may have to wait until the lease is up to lease another horse, and you could be afraid to ride that horse. I would recommend you lease a horse when you are an intermediate or advance rider.
So anyway, say I take barrel racing lessons and I am an intermediate rider. I know some things about horses and horseback riding, and I decide I want to lease a horse. I want to lease a barrel horse, but it should probably be for my experience level.
Say I wanted to compete in barrels on a horse I want to lease. I would want to lease a horse that has been in competition before, not one that has never competed. The horse should probably have competed on barrels, not on jumping, or something other than barrels.
Finally, you would want to make a deal with the owner of the horse you will be leasing. So, for instance, I want to compete on a horse for barrel racing and I am an intermediate rider. I want to be able to lease a horse that I can practice on at any moment. I want to be able to have an arena, barrels, and anything I may need to practice barrel racing with the horse I want to lease within reason-ability.
Last but not least, you want to pick a horse that fits you best. If you like a challenge, you may want to get a horse that can give you a challenge. If you just want a horse that will compete on barrels and do what you ask, you might want to lease a horse that has done several barrel racing competitions and is a pro at it.
I hope I could help, but these are just some things to know when leasing a horse, and what you should look for.
It greatly depends on the discipline and level of riding.
If I were to look for a full lease on a rated hunter horse, I would expect full rights to ride and show said horse. I would expect to pay all additional expenses such as board, training, farrier work, and of course, my lessons and shows.
If I were a young rider looking to lease a beloved lesson horse for the first time, I would look for a safe and quiet guy and maybe hope to have board and some care included as I would not yet have the experience needed to take care of a horse full-time or to see a subtle unsoundness or bout of colic.
When leasing a horse you get to choose what fits you best! As a professional, you should take note of what other professionals in your industry and of similar niche are doing. Luckily, there is always wiggle room in leases and you can often do what fits you, your horse, and your rider the best! Good luck!