I doubt it. You will have to accept that there are no "definitive words" for songs like this (and for a great many others), where a fair number of differing examples have been found in tradition and where (so far as is known) no early texts exist. There are 19th century broadsides, of course, but they are as obscure as many of the traditional texts; and may perhaps themselves have been harvested from tradition.

Are you expecting the words "as sung by Julie Murphy", or a reasonably full and coherent text from some other source? Since the sleevenotes of that particular record, as I understand it, name no source for the version of the song they have arranged, the sensible thing would be to ask Julie, I'd have thought.

Meanwhile, there are a few broadside editions to be seen at Bodleian Library Broadside Ballads; they can be found under the titles Sweet Lemminy and The lad I adore. There's also an "answer" to the song that doesn't seem to have lasted in its own right. It doesn't throw much light on the subject, except to indicate that the song was sufficiently current in 1819 for it to be worth Catnach's while printing a spin-off as part of a larger songsheet.