Like many traditional songs of soothing, “Deep Blue Sea” is about death. Don’t believe me that this is a pattern? Sing “Rock-a-bye Baby” all the way through. See?
Personally I think this has something to with the fact that the real “audience” for a words of a lullaby is the person singing it. And in those quiet and tired and sometimes desperate hours of trying to soothe a crying baby, it makes sense to me that the person singing the lullaby might feel a certain freedom in letting the words be darker than the melody.
Other ideas: death and sleep are linked in many cultures. Death is seen in some contexts as a form of release.
I welcome your thoughts on this in the comments below.