My unabridged dictionary has three meanings for lea:

pasture
scythe
a certain measure of thread or yarn, for linen, 300 yards.
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Here are Mary Black's lyrics:

First when I came to the town
They called me young and bonny
Now they've changed my name
Called me the Leaboy's honey.

I'll dye my petticoats red
And I'll face them with a yellow
I'll tell the dyester lads
That the Leaboys I've to follow.

It's over hills and dales
And over dykes and ditches
Say will I like the lad
Who wears the moleskin breeches

The black horse draws the cart
And he's as proud as any
Say will I like the lad
That drives them on so canny

Feather beds are fine
And painted rooms are bonny
But I would leave them all
To jog away with Johnny

Oh, for Saturday night
It's I that'll see my dearie
He'll come whistlin' in
When I am tired and weary.

First when I came to the town
They called me proud and saucy
Now they've changed my name
Called me the Leaboy's lassie.
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We can conclude from this that both the lassie and the leaboy had trades that kept them on the move. And that the leaboy drives a horse and cart.

Frankly, I wonder if even the person who wrote the lyrics knew what a leaboy actually was.

(That leaboy is the same as lichtbob is not very convincing.)