The Lynn mentioned is, in fact, Kings Lynn, Norfolk, England.

The song is about something. In English mediaeval tradition members of three trades were thought of as ignoble. Millers, weavers and especially tailors (see Chaucer).

Whereas millers and weavers get their just desserts in the song, the tailor is too much of a rogue, so he ends up enjoying it.

This is it as I sing it.

King Arthur (A Farmer) Had Three Sons

A farmer had three sons
Three sons to him were born
And he came home tight in the middle of the night
And threw them out of the door

Ch:
And threw them out of the door
And threw them out of the door
And he came home tight in the middle of the night
And threw them out of the door

The first was a jolly miller
And the second was a weaver of yarn
And the third, to be sure, was a little tailor
With the broadcloth under his arm

Ch:
With the broadcloth under his arm
With the broadcloth under his arm
And the third, to be sure, was a little tailor
With the broadcloth under his arm

The miller, he stole corn
The weaver, he stole yarn
And the little tailor boy, he stole corduroy
To keep those three rogues warm

(ch)

The miller, he was drowned in his pool
The weaver, he was hung by his yarn
But the devil ran away with the tailor one day
With the broadcloth under his arm

(ch)

The miller still drowns in his pool
The weaver still hangs by his yarn
But the little tailor boy, he skips through hell
With the broadcloth under his arm

Cheers! IanC