I have only come across a couple leather faced pads in my life, a fairly rare way to treat a butt in my mind. I have not installed one myself but on the ones I have seen the leather seemed quite similar to what I use on leather covered pads, 1&1/2 to 2OZ top grain pigskin:

https://www.zackwhite.com/Full-Grain-Pigskin-Lining

I would use the same glue I use for covered pads, barge cement:

https://www.myshoesupplies.com/prod...Qr6et7gIVjb3ACh0RyAV3EAQYFSABEgI_q_D_BwE

Keep us informed as to what you decide and how it works out.

Steve