Songfacts®:

• This is a sequel to Costello's 2010 track "Jimmie Standing in the Rain," which tells the story of a vaudeville performer in the '30s who has fallen on hard times. In "Under Lime," it's 20 years later and he is attempting a comeback, but having a rough go of it. He agrees to appear as the "mystery guest" on a TV quiz show, where a young, female production assistant does her best to dodge his advances and get him to the stage. Once on the show, he make a fool of himself, setting back his career even further.
• The phrase "under lime" has a dual meaning (as we've come to expect from Mr. Costello). It could relate to the "limelight," meaning on stage under the lights. Lime can also be used to hasten decomposition when burying a body, so if you're "under lime," you are dead and buried.
• As we hear about the song's vaudevillian character's seedy interaction with a production assistant it's difficult not to label him a misogynist.
  
  In the violent strip of an undressing room
  She loosened his grip and started
  Tell me your story if you feel so inclined
  He was a mess, almost resigned
  
  "Those kinds of exchanges have been in my songs all along, not because I'm that person, but..." Costello nodded to The Independent. "I wish I could write like Lionel Richie – heartfelt love songs with nothing insincere about them. But that's just not what I do. I find the other angle, or maybe two or three different angles in the same story."