"Greased Lightning" is the name of a song from the musical "Grease." It's also a colorful way to describe something that's really fast. "Jamaican sprinter Usain Bolt was like greased lightning when he won the gold medal in the 200-meter finals in London," would be one way to use the term properly. "Nic Cage's fall from Academy Award-winning star to some strange approximation of a mid-'90s Al Pacino after a five-day meth bender was like greased lightning" would be another.
It works because lighting usually flashes in an instant. If there were some way to grease it up, that would make lightning even faster. And people love to exaggerate in speech. Just to be clear, there's no such thing as greased lightning. The term was first used in the 19th century English newspaper with the very long name of The Boston, Lincoln, Louth & Spalding Herald. An 1833 article included the sentence,"He spoke as quick as 'greased lightning'" [source: Phrase Finder].