Technically, Dad, the theme from Gilligan’s Island is not a lullaby. But you can tell me again what happened to The Minnow.

Baby boy max, wearing a black Polo outfit, sits on a BoppyNewbornLounger, while giving insight to his father
(Gilligan’s Island Intro [YouTube])

And, for the record, nor is Spider-Man [YouTube].
And not The Brady Bunch Theme [YouTube] either.

What other songs do you actually know?