Richard Blakeborough gave a text from Cleveland in his book Wit, Character, Folklore, and Customs of the North Riding (Oxford University Press, 1898).  I haven't seen the book yet, but F. W. Moorman, Yorkshire Dialect Poems (1673-1915) and Traditional Poems (Yorkshire Dialect Society/ Sidgwick and Jackson, 1916) quotes it, commenting:

"The text of this version of the Lyke-wake Dirge follows, with slight variations, that found in [Blakeborough's book] (p. 123), where the following account is given: "I cannot say when or where the Lyke Wake dirge was sung for the last time in the North Riding, but I remember once talking to an old chap who remembered it being sung over the corpse of a distant relation of his, a native of Kildale.  This would be about 1800, and he told me that Lyke-wakes were of rare occurrence then, and only heard of in out-of-the-way places. ... There are other versions of the song; the one here given is as it was dictated to me.  There is another version in the North Riding which seems to have been written according to the tenets of Rome; at least I imagine so, as purgatory takes the place of hellish flames, as given above."

CLEVELAND LYKE-WAKE DIRGE

This ya neet, this ya neet,
Ivvery neet an' all;
Fire an' fleet an' can'le leet,
An' Christ tak up thy saul.

When thoo frae hence away art passed
Ivvery neet an' all;
To Whinny-moor thoo cooms at last,
An' Christ tak up thy saul.

If ivver thoo gav owther hosen or shoon,
Ivvery neet an' all;
Clap thee doon an' put 'em on,
An' Christ tak up thy saul.

Bud if hosen or shoon thoo nivver gav nean,
Ivvery neet an' all;
T' whinnies 'll prick thee sair to t' bean,
An' Christ tak up thy saul.

Frae Whinny-moor when thoo mayst pass,
Ivvery neet an' all;
To t' Brig o' Dreead thoo'll coom at last,
An' Christ tak up thy saul.

If ivver thoo gav o' thy siller an' gowd,
Ivvery neet an' all;
At t' Brig o' Dreead thoo'll finnd foothod,
An' Christ tak up thy saul.

Bud if siller an' gowd thoo nivver gav nean,
Ivvery neet an' all;
Thoo'll doan, doon tum'le towards Hell fleames,
An' Christ tak up thy saul.

Frae t' Brig o' Dreead when thoo mayst pass,
Ivvery neet an' all;
To t' fleames o' Hell thoo'll coom at last,
An' Christ tak up thy saul.

If ivver thoo gav owther bite or sup,
Ivvery neet an' all;
T' fleames 'll nivver catch thee up,
An' Christ tak up thy saul.

Bud if bite or sup thoo nivver gav nean,
Ivvery neet an' all;
T' fleames 'll bon thee sair to t' bean,
An' Christ tak up thy saul.

This would seem to confirm the reading fleet, rather than sleet.  I think that Moorman's "slight variations" are no more than modifications of some of the spelling.  Again, no tune appears to have been recorded.  The full text of Moorman's book (and of his Songs of the Dales, which includes his poem The Dalesman's Litany, often imagined to be a traditional song) is available online at Dave Fawthrop's  Yorkshire Dialect Poetry.

So far as the Young Tradition's set goes, the notes from The Young Tradition (1966) read:

"The dirge as we sing it is an adaptation of Aubrey's manuscript version of 1686...Whether the dirge was sung, chanted or recited over the corpse is not clear; there is no evidence of an air to the dirge in the tradition.  The tune used here was given to us by Hans Fried, who heard it long ago from an old Scots lady, Peggy Richards."  (Notes quoted from Gary Gillard's  Young Tradition pages) [Now at https://mainlynorfolk.info/peter.bellamy/songs/lykewakedirge.html]

Information that we now have makes it clear that there was a melody, but that it was not recorded.  Whoever Hans Fried may have been, the "old Scots lady" from whom he got the tune had certainly learnt it from the widely-available book I mentioned earlier.  Since it was a song unknown in tradition in Scotland, she can scarcely have had it from any other source, and "long ago" would, I suppose, have been any time during the 20th century.

There are a number of candidates for "Whinny Muir"; Winmoor, near Leeds, is one.  There was also a Whinny Moor mine in the Wakefield area in the late 19th. century; neither of these really counts as North Yorkshire, so any further specific information would be welome.

Malcolm