The original lining appears to be a thin layer of the orange "leather" glued to some thick tan fabric (which you can see in the photo). It's the orange part that's peeling; the fabric part is fine if a bit sticky. I do think the fabric bit provides structure so I'd probably try to just peel off the orange. This is good as it means I can sew a new lining to the fabric and not to the suede.
There is a large zipped center pocket that goes the length of the bag and divides it in two. So even if I covered over the side pockets I'd still have that compartment. It does mean I would have to stitch in 2 separate fabric linings though, one for each side. The lining inside that zippered compartment seems ok because it's more protected.
Una, I'd totally go that route but I think the affected area is too big. I'll keep the carpet tape in mind though!
Hmm, must consider further. This might be a good summer weekend project. On the other hand I have a history of taking on complicated DIY projects and ending up completely overwhelmed. In the past this had led to the, " mommy, fix it!" solution, lol. But my mommy is 3000 miles away and has better things to do!