I think all my teenagers can complete the Brillig line. I know my wife and I can.
My daughter worked for weeks to memorize the "Breathe deep the gathering gloom" poem from Nights in White Satin (she memorizes slowly).
You can also sing the doxology ("Praise God from whom all blessing flow...") to Hernando's Hideaway.
My wife says that in a lit class in college, the teacher defined a "lyric poem" as one you could sing. At that point one of the girls in class stood on her chair and started singing "Maid of Athens, Ere we part" to the tune of "Rock of Ages, Cleft for Me."
Switching lyrics and melodies is a lot of fun.