They are associated in theme, though. The Lute Book Lullaby is Mary's lullaby to the Christ child. And the Coventry Carol is the song of the mothers of the Holy Innocents (whose feast we celebrated yesterday)--it uses the lullaby motif as the chorus, turned into mournful song of all that is lost.
This is one of the better videos I have seen of the Lute Book Lullaby. It is best sung with a small choir, so that every voice shines. Though the harmonies are medieval in character, the carol was written in the late 1900s. The best recording I know was done by the great counter tenor Alfred Deller, in his Consort's wonderful Christmas recordings.
The Coventry Carol is of course well known by most Christians. It is from the 16th Century, part of a Mystery Play. I like it best when sung by only women.