No one seems to have looked in the Oxford dictionary.
The words layland, leyland, leland, leylond and leyk-(land) are all synonyms of Lealand.
Lealand is fallow land, or land laid down for grass. The word first appeared in print in the 14th century (glossed into modern English as leylond). I may have missed some of the various spellings. (OED)

Add comments by Malcolm Douglas to round out the definition and its history.

In the sense of the song, 'laylums' is just a corruption.