A lot depends on how the materials were catalogued and how they are put online. We, for instance, do not have the same system for the online catalogue as we do for the staff in the library. So we can often find things that the patrons can’t find on their own on the online catalogue. Also, a lot depends on how the items were catalogued by subject. Cataloguing software changes periodically—many of us are about to change again—and if the person cataloguing the item didn’t mark a picture book about an alligator family as being “subject–alligators–fiction” then it won’t show up when you do that.
Worldcat can be helpful, if you want to go there and search “alligators” then unselect the things like “large print” “e-book” etc, then you can go down and check “fiction” and “juvenile” and you’ll get 1200 or so titles; if your library is in worldcat you can log in and see what is there. Mine isn’t. But you can mine for a few titles and see if your library has them.
Also, try to do a catalog search if you can that gives you an index listing; it’ll depend on what you have but sometimes “advanced search” will produce this. Then you can scroll down under the heading “alligator” and search for “fiction—juvenile” and see what is there. None of that will however tell you if it is a LIVING book–that isn’t a subject heading! and also some of the nonfiction books likely ARE living!