My own experience is to listen to the original song or someone's cover version over and over. Sing along with it, and viola, just like that it is memorized. I listened to Sinatra's Ultimate collection release so many times, when one song ends, I can hear in my mind the first notes of the next song before it starts. I don't think there is a secret method. It really is just repetition. The big acts are all using teleprompters. You just never know when you are going to forget a lyric so better to be safe than sorry. Most local people I see use iPad or some version of written music as a guide or reminder. Just like playing guitar instrumentals once it is in the muscle memory it becomes almost automatic. Then you can focus on the emotional side of it and improvisation etc.

My wife asked if I had seen the dog bowl. I told her I didn't even know he could.