“The Lost Daughter” is a searingly honest examination of the inner life of a mother, an ordinary mother, and Olivia Coleman in the central role is brilliant. Holidaying on a Greek island, 48-year-old Leda butts up against an extended American family, steeped in menace, and when the daughter of one of the men goes missing, the subsequent events build up in shock and fear. Leda, beset with memories of a fraught time when she was a young mother of two, wresting with career aspirations, takes steps that seem destined, in this moody film, to brook disaster. The fact that Maggie Gyllenhaal based her screenplay on an Elana Ferrante novel, just the kind of roiling internal examination that movies seldom attempt, and then directed the film, offered a great chance to make an arthouse classic. But a looseness of narrative control and the arbitrary use of symbolism undercut the power of The Lost Daughter. Nonetheless, it does grip and comes recommended.