Memory is the second thing that goes... I Forget the first.
For starters; analyze the structure of the lyrics.
1. Example Mack the Knife is composed of half lines. "Oh the shark......has pretty teeth." "And he keeps them.....pearly white". Ignore all the dears, babes and other extraneous verbiage that characterize various artist's covers. You can add them back later if you must.
2. Check for internal rhymes and assonance(s)? Is the external rhyme scheme for couplets or alternate lines.
3. Is there a repeated refrain? Example: Verse 1 of "I've been Working on the Railroad":
"I was down.... in Mobile Town",
"Working on the Levee",
"Levee's done..... but I'm still here",
"Working on the Levee". ch: "Now I've been working on the ........"
4.Listen to several videos of the song to determine the meter. In Mack the Knife you'll note the number of syllables in each half line vary.
Iambic Pentameter is a normal speaking cadence in English: "The Rain in Spain.... falls mainly on the Plain". This example also uses internal rhyme in both half lines.
Secret Number 1. If you maintain the meter and keep the rhyme scheme; It doesn't really matter if you forget the some of the words. The song will still hold together.
Secret Number 2. The most common lyric in English Song is "La, La, La." (Remember to use enough "La"s to maintain the meter.