Are lyrics poetry? Billy Collins says not.
I can think of a songwriter or two who would take umbrage with that.
I'm not sure it's all that clear cut, and it doesn't seem that The Book Bench is, either.
I must say that I think there are some song lyrics that are far more poetic than some poems I've seen published. I'm firmly setting myself in the grey area on this one, and I think anything else would be kind of silly.