Well, I seem to have answered my own question. I've got the sqlite executable running, so I guess the library should be fine too. (I'm working towards a lua app with a database backend.)
Apparently SQLite is a pain to cross-compile because the Makefile you get out of the box tries to execute some of the files it creates halfway through the process, which of course doesn't work. I used a variation on
this solution, with the Irex SDK tools installed as
hansel described. I'll admit I don't entirely understand what I did, but it seems to have worked.