All that can presently (June 2022) be gleaned about Lizzie Rimmer from sheet music covers and by Internet searching is that she was presumably an English actress/singer who has been featured on just one work namely Farewell, if We Ne'er Meet (1896) music by J.M. Harrison, words by H A Duffy and published by Francis, Day & Hunter, London W.C.2, England
Surfers are welcome to contribute any further information about this performer.