It's been quite a while since I've posted anything but this thread caught my eye. I've always had a knack for remembering lyrics and at age 72 I'm surprised that the ability hasn't left. When I play out I only carry a notebook with names of songs that I play. I just looked through it and have a list of 65 of the songs that I've written and 68 covers that I like playing. Some of them I haven't played for a long time but I estimate I could play 58 of my songs and 64 of the covers and remember all the lyrics. My issue for some songs is remembering what key to play it in and the chord progressions.
When I learn a song I first concentrate on remembering the chorus/hook. Nearly all the songs I play have verses that are similar to chapters in a book or story that relate to the hook, so I then try to remember some key words in each verse that are easy to recall and trigger my memory of how the story "flows". Works for me. Your mileage may vary.