Knowing where material was quoted from really does help. In this case, Lloyd quotes two verses of The Unfortunate Rake, selected because the previous song discussed was The Flash Lad, which also ends with a military-style funeral. He then comments, "This song was heard in Dublin in the 1790s". He doesn't give a source for the two verses quoted, but there's no particular reason to think that he is saying that those two verses in particular are from 1790s Dublin; merely that the song in general can be traced back that far. The same superficial ambiguity occurs in the notes to the Sedley collation mentioned earlier, and has, as we have seen, led to some confusion.

So far as I know, (not having seen the Lomax book) the dating to 1790 derives initially from Patrick Weston Joyce; in his Old Irish Folk Music and Songs (1909) he reproduces one stanza, with tune, noting "From Mr. W. Aldwell of Cork ("Dec. 17, 1848"), who heard air and song sung in Cork about the year 1790. He remembered one verse of the song, which, as Forde remarks, is curious for the absense of rhyme".

My jewel, my joy, don't trouble me with the drum
Sound the dead march as my corpse goes along;
And over my body throw handfuls of laurel,
And let them all know that I'm going to my rest.

Distant memory is not always the best way of dating songs; really, all we have here is hearsay. It seems that the same tune was printed in Crosby's Irish Musical Repository in 1808 (ref. David Atkinson, The Unfortunate Rake, in Root and Branch no.1, 1999) but that doesn't necessarily mean that it belonged to the Unfortunate Rake at that time. Only someone who has seen the book could tell us more about that.

When I Was On Horseback, incidentally, was recorded by Peter Kennedy from the traveller Mary Doran, near Belfast in July (according to Kennedy; the Roud Index gives it as August) 1952. It appears to be the only example found of that particular branch, which may have to be considered -unless someone comes up with another- a dead-end for your purposes.