This sounds a bit silly, but I think you've heard different pronunciations, OP, just because there are different ways of saying it.
In Irish the word leanbhán is said like this in some dialects
forvo.com/word/leanbh%C3%A1n/
But in Ulster Irish this is a bit different as Ochon mentioned - for a start they don't pronounce án as awn as the other dialects do - and it's an Ulster song. The letter l is slender (as it's next to an i or e) and in Irish this is not said the same as an English letter l...hence ly was used to transcribe as MarDhea said. You can hear the difference in the l sound in the link above.
The song is in English though, not Irish, and leanbhan is somewhat anglicised without its fada and would be said more like lan-van then. This is how Luke Kelly says it in his version I think. Singers will tend to use their own Irish or Hiberno-English dialect when singing so that's why you're hearing different versions. And the number of syablles have to match the song too as MarDhea said, so there's probably some adjustment there.
As a diminutive án is still seen today in names -Ciarán, Aodhán, Caolán, Ŕónán etc.
It's a lovely song.