I seriously doubt that Sinatra could remember all the words to ALL the songs he performed over the years, even those that were top hits and he performed thousands of times.
Gary
I saw Sinatra at the Providence Civic Center 35 years ago, 'in the round' ... Second row seats ... I could see his monitors that had the lyrics to every song scrolling - including the so called 'ad-libs' he would throw in ...
On occasion during a music awards show, I've even caught a glimpse of a lyric monitor for a pop star singing their latest hit ...