The research I done suggests
The U.S. Copyright Office requires that the work must contain a significant amount of human authorship
When registering, you should disclose that the lyrics were generated with the assistance of AI
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But what if all of the lyrics were AI generated but all of the music was human generated. That could include inputting chords into BiaB, selecting a style, then adding other tracks via guitar, bass, keys, etc. Or what if all of the instrumentation was done "organically"? Wouldn't these scenarios indicate a a significant amount of human authorship? I would think so but hey, I'm just a guitarist.
I think the group most likely to make money off of AI are lawyers. YMMV