Vehicle lock-up control method and control device

A vehicle includes an engine, a continuously variable transmission and a torque converter that has a lock-up clutch. The torque converter is arranged between the engine and the continuously variable transmission. In this vehicle, when an engagement request of the lock-up clutch is issued, an initial-motion lock-up control is executed, whereby engagement is achieved through slip control that increases the lock-up capacity and gradually reduces the slip rotational speed, which is the input-output differential rotational speed of the lock-up clutch. During the slip control of the initial-motion lock-up control, if the slip rotational speed enters a smooth ON control region that is at or below a first set value, a second engine torque reduction control is executed that reduces the torque of the engine below the normal torque that is applied in response to a driver's request.