An autonomous controller for lateral motion includes a vehicle positioning module that calculates a lateral departure degree from the center of a virtual line after a line is lost using position information of a vehicle. The position information is derived by data obtained from the vehicle which is traveling. The controller also includes a driving route determination module that determines the virtual line connecting waypoints previously generated on a map for a section where the line is lost to connect an old line with a new line. A lateral control module then performs lateral autonomous control of the vehicle in a direction where the lateral departure degree is minimized to cause the vehicle to follow a driving route connecting waypoints set on the virtual line to travel.