Some use 3M spray adhesive. Others use white glue. Contact cement holds like Superman. If the cloth is thin however, the glue soaks through. I find that unsightly. Others don't care. I am known to be fussy, so take it for what it is worth. I also do not like lining stained by dye. I dye the leather before adding the lining.
I have been using 100% cotton heavy awning canvas for lining. It will resist wearing through, and gives more body. I wash it, heat dry it, and iron it flat before use. You don't want it shrinking later.
Note that if the cloth is not adhered somehow, you can get a hole in the cloth and lose items between the lining and leather. Not a fun situation.
All of my lining is stitched into the seams, easy to do with an inside-out bag. Are you thinking flat-sewn? Think through how you will treat edges like the top of the front panel. I use a rolled edge to hide the raw cloth edge.
Just some ideas. Good luck with your project. I am sure that some very skilled leatherworkers will weigh in here with some super ideas.
Yes, that buckskin is like a rubber band. :-)
God Bless, Marc