Greetings from Fullerton, California!
As a fan and friend of Fritz Leiber, Jr. back in the 1970's and beyond, I too had the opportunity to ask him (by letter) several questions about his and his characters' names.
Please see pages 3 and 4 of my "Eldritch Leanings" fanzine, Issue Number 5, from 2-February-1977 with quotes from a letter I received from Fritz Leiber, Jr He confirmed that it is Li/ber ("li as in like"). on 3-December-1976:
Page 3: https://www.flickr.com/photos/cthulhuwho1/4864863926/in/album-72157624536159977/Page three of my fanzine contains the relevant quotes.
Page 4: https://www.flickr.com/photos/cthulhuwho1/4864864214/in/album-72157624536159977/
Q. ... Li/ber (li as in like). F.L. Correct!
Eldritch Leanings - Issue #5, 2 February, 1977
PS Anyone. Anyone interested in Fritz Leiber, Jr., might also enjoy this section of my Blogthis section of my Blog devoted to him; and, you might just spot me in a couple of the pictures with him too.: https://www.flickr.com/photos/cthulhuwho1/sets/72157625066410282/
PPS I I can't believe I'm still around to post this about Fritz!
Will Hart