Here are some suggestions:

Choose songs with a logical story to tell.

Choose songs with lots of rhyme.

Sing them as you work around the house.

Focus on awkward lines which are hard to remember. Sing them repeatedly.

Have "notes" on stage which consist of only one word or two per verse, written large, so you can sneak a glance without being obvious.

It's all very well to say that So-and-so forgets words onstage. So-and-so is famous, and people are willing to overlook any flaws. You are not, so you are right in wanting to improve your memorizing skills.