I can't answer your questions but I have also heard that blue and white striped lining commonly referred to as "mattress ticking" and it is often seen in accessories from the late 1980s.
I don't know if you want to invest money in having it repaired, but I have a small Bonnie Cashin bag that also had the lining (and leather) slipping out from under the metal of the kisslock frame. I was afraid to try and fix it myself so I took it to a trusted shoe repair craftsman (a cobbler).
He told me that he could try to secure the leather and lining under the kisslock frame but there was a chance that he would bend the metal. He said that
Coach must have had a special tool designed to clamp the leather and the lining inside the frame, but nobody has a tool like that nowadays - unless Coach still has it.
He said that he would not even attempt to repair it if the kisslock frame was made of cheap, flimsy metal - but the Coach frame was made of strong metal so it might be okay. I told him to go ahead and try to fix it because I didn't want to carry the bag with the leather and lining slipping out.
He was able to fix it beautifully without damaging the bag, so if you have a trusted leather worker in your area, you might ask him/her for an opinion about putting the lining back inside the frame of your eyeglass case.
You can see photos before and after the repair of the frame of my little Cashin bag at the link below. I had him fix the frame before I embarked on rehabbing the bag so it looks kind of dirty and squashed but the bag eventually rehabbed quite nicely:
https://forum.purseblog.com/threads...-beautiful-rehab-reveal.742282/#post-21502370
I wear glasses daily and that is a very nice vintage coach eyeglass case in an unusual color. I am sure that many Coachies, including me, would very much like to own it ourselves, congratulations!
