I have also seen the name Lizzie spelt as Leezie in printed music, including the Child Ballad book I found it in about 20 years ago, if my memory serves correctly.

Lovely tune, despite its simplicity, although the version I know has a few more twiddly-bits (deeply technical term, there) in the melody than the DT version.

Helen

P.S. Do a search on Lindsay rather than Lizzie, or go to the tune titles.