I think you mean
Three To Get Deadly, unless your version has a lowercased title.
👁 Smile :)
Ok, I read the passage on page 128, 129 and 130. Stephanie uses a key from Uncle Mo's apartment to get into Mo's store and she locks the door behind her and describes the situation to Morelli: "When Ronald Anders tried to get in, the door was locked. At first it sounded like he had a key, but the door wouldn't open. He fiddled with it for a couple minutes, and the door clicked open."
So a
sticky key is literally a key that sticks. Normally this is a key that has been duplicated from the original to be used as a backup. Often these keys are imperfectly machined and seldom used, so it doesn't work was well as the original key from the manufacturer. You have to jiggle it around to finally get it to open the lock.