A work in which a satirist creates new, humorous lyrics for a well-known song would be an example of

reduction ad absurdum

caricature

sarcasm

parody

This would be an example of a parody. According to the dictionary, a parody is "a work created to imitate, make fun of, or comment on an original work". This would include making humorous lyrics for a well-known original song. One example of a well-known artist who makes parody music is Weird Al Yankovich.