The first horse I leased was older (mid-20's or so) and got retired after I had ridden her for a year or two, so I moved on to a new horse. I was definitely a beginner when I started riding her, and she was great to learn on. I don't think I would have been able to handle my 2nd lease horse if I had tried starting with him!
He was younger, but was suspected to have navicular disease and the owner decided to try a barefoot trimmer with him to see if he could be made more comfortable. After several months of not being able to ride him consistently I decided it was time to move on to another horse. It turned out later that whatever his issue was, it was confirmed by x-rays that it wasn't navicular, but to this day he's still lame some days and not-so-lame others. I did click with him very well and if I ever get my own horse property I'd love to buy him as a companion for my horse.
The third (and final) horse I leased was fine health-wise, but had a bit of a bucking problem I was pretty glad when his lease was up.
I lucked out that I had access to ride my leased horses pretty much whenever I wanted (even though the first 2 were technically half leases). None of them really had solid dressage foundations prior to my riding them, so I always ended up starting at the basics again and could never quite make it to 1st level before switching to a new horse for one reason or the other. The horse I ended up buying had some informal dressage training, but hadn't ever competed. I started him at intro level last year, and we just rode in our first recognized show at 1st level a couple months ago