I put a hydraulic lift on my 125 last summer (2019) after I found one at the flea market at Red Power Roundup.
You use the same lift rockshaft as the manual lift, except that the handle is cut off where it comes out of the lift mechanism.
I took some pictures of installed hydraulic lifts at Red Power to use as guidance and I also have a copy of the Hydraulic Lift Installation Manual that I could email to you, if you would be interested. No charge of course, but I would point out that the manual didn't answer all my questions, some things I had to figure out on my own, but it did help some.
Mine is on and working, so I could take some pics of specific things if you need me to. Internal parts for these things are scarce.
I bought a new belt for mine, but I do not recall the number. If you can give me a day or two, I can walk out to the shed and see if the belt number is legible on mine. You will have to move the engine to get the belt on.
EDIT: OK, It's a slow day so I went out and checked on that belt.
IH 38616 I got it at the local Cub Cadet Dealer. Same dealer also made new hoses for me.