The version of "Little Liza Jane" in the database is sung to a different tune from the version Joe Offer quotes in the post, so it doesn't help the person who wants more verses for it.
As long as we're preferring Liza Jane songs, the one I like is the one that goes "whoopee Eliza, pretty little girl/whoopee Eliza Jane/whoopee Eliza, pretty little girl/she died on the train." I've decided that it must really be "she 'rived on the train," because she's not dead in the song. Anyway, it has a kind of counter-chorus I find compelling and witty: peach is like a cherry cherry like a rose how I like that pretty little girl goodness gracious knows
The tune's prettier than either of those others too.
Lucy