I absolutely agree with Bear and I have made a 'lot' of bags. I would actually make the lining as much as 3/8-1/2 inch smaller in width and height depending on what type of batting or stiffener you use. If you use something like Bosol, it is a good 1/8th inch thick.
I also agree about finishing seams on fabric that frays easily. I have zig zagged the edges of frayable fabric before putting a bag together. It's an extra step but well worth it in the long run.