While most of the 70+ branches are closed Sundays, there are some 8 or 9 that are open from 1-5 on Sundays. E.g. the branch on Robertson, a few blocks south of Pico.

The hours for all branches are on the following page; to find the ones open on Sunday, just search on the page for:

Sun: 1-5

https://www.lapl.org/branches

Also, the Beverly Hills Public Library -- which is, of course, not part of the LA library system -- is open 12 - 6 on the weekends:

https://roxbury.beverlyhills.org/