Lock-up clutch control method for vehicle, and lock-up clutch control device for vehicle

A vehicle lock-up clutch control method is performed in which an output of an engine is transmitted to an automatic transmission via a torque converter having a lock-up clutch. The method includes controlling a transmission torque capacity of the lock-up clutch such that a slip rotation speed of the lock-up clutch becomes zero after the lockup clutch is brought into a non-engaged state immediately after starting an accelerator operation, and when the accelerator operation is carried out during a fuel cut of the engine or in a state in which a road load and a driving force of the vehicle are balanced, and after completion of a downshift when the automatic transmission is downshifted while executing a slip control of the lock-up clutch from the non-engaged state to an engaged state during the accelerator operation.