You don’t have to be able to read music to be a musical genius. You can learn to read music in about an hour.
I would say that as a Beatle, John Lennon was a very good songwriter, with moments of brilliance (She's Leaving Home comes to mind.) But a genius? Nope. I believe Paul McCartney was the better songwriter. His songs seem to have a longer, stronger shelf life. What song does Lennon have to match Let it Be, or Hey Jude, or the Long and Winding Road? Or hell, even Birthday? But would you say McCartney was a genius? JS Bach? Hell no. A very, very good pop songwriter. Lennon? At times a good songwriter.