Entering “Ireland-America: The Ties that Bind,” housed in Lincoln Center, one of New York City’s finest arenas for the arts, it is easy to get overwhelmed. We’re dealing with more than two centuries of performing arts history, after all. A television screen is on the right; posters and display cabinets are straight ahead; a sign describing the exhibition is just to the left; a playing fiddle and the sounds of feet tapping in tune can be heard. Head to the television and sit on the bench. The next 18 or so minutes will be thrilling as a video reel plays a representative variety of clips, including Michael Flatley performing in Lord of the Dance, a short interview with Liam Neeson, and a clip of Jack Lemmon and Walter Matthau in a 1974 production of Sean O’Casey’s Juno and the Paycock at the Mark Taper Forum in Los Angeles.