A good friend of mine is a harness maker. He apprenticed at CW, then moved to Ohio to work at the Ohio Historical Society while I was there. He always lines his nicer work with woolen or heavish cloth, and adhears it to the leather with 3M fast tack adhesive. I know it is not PC, but that is what he uses. Possibly back in the day, a hide glue might have been used. At any rate, I have used the same method, and the results are great...No worries about ripping a saggy lining.
Just my 2cents....Dan