Mrs. Miller can’t sing — but don’t tell her that. Based on the real-life story of Elva Miller, Mrs. Miller Does Her Thing is a portrait of a devoted, warbling songstress whose operatic, off-key singing became an unlikely pop phenomenon in the 1960s. This play by Pulitzer Prize winner James Lapine (Sunday in the Park With George) romps through golden oldies like “A Hard Day’s Night,” “Monday, Monday,” and “Downtown.” Leading the way is Emmy and Tony Award winner Debra Monk (Mozart in the Jungle). At her side as Mr. Miller is Tony winner Boyd Gaines (Gypsy).