There is an arrangement by Byrd, and one of the 20th century by Peter Warlock. What do you mean by "formerly attributed"? Is Byrd out of the running now?

A website called Land of Nursery Rhymes provides some additional text at http://www.landofnurseryrhymes.co.uk/htm_pages/Lullay%20Lullay.htm:

My darling dear, my daisy flower,
Let me, quoth me, lie in your lap.
Lie still, quoth she, my paramour,
Lie still hardly, and take a nap.
His head was heavy, such was his hap,
All drowsy dreaming, drowned in sleep,
That of his love he took no keep,
With hey lullay, lullay, like a child,
Thou sleep'st too long, thou art beguiled.

Unfortunately, whoever runs that site couldn't be bothered to say where they got it. It could have been made up last week by the milkman for all we know, so don't assume it's genuine until someone confirms that.

Did the Boston Camerata credit their source for text and melody, or did they keep it a secret?