The title of the thread pretty much says it all, but to be perfectly clear, I’m not asking for who owns the copyright to the music, nor who owns the copyright to Lennon’s recording of the song. I just want to know who owns the rights to the lyrics. That is, if someone wanted to reprint the lyrics in a book, to whom would they write for permission?
Song music and lyrics are both copyright together and the rights are normally controlled by the song’s publisher, just as with books, unless those rights have been reverted to the author.
“Imagine” appears to have been published by Northern Songs, which is now a unit of Sony/ATV Music Publishing LLC.
Their FAQ page gives contact information for various uses, including print licensing.