There’s a brief mention of libraries in the Archie story “Lost and Found,” which first appeared in Betty and Me 183 (June 1990). Archie and Betty are looking for his tennis racket in his room and he finds an old library book.
Archie’s usually broke, so even a small fine could drain his savings.
I read this in Archie (Jumbo Comics) Double Digest 298 (June 2019). It was written by Hal Smith, penciled by Stan Goldberg, inked by Rudy Lapick and lettered by Bill Yoshida (no colourist is given). It is copyright Archie Comic Publications.