1. A lane determining device, comprising: a controller that: obtains vehicle position information indicating a current position of a vehicle; based on the vehicle position information, obtains road information including positions and forms of lane markings around the current position of the vehicle; based on the road information, determines whether a branch point exists on the road in a forward direction of the vehicle; if a branch point exists, obtains image information of an area before the branch point; and determines whether no lane marking is imaged or is partly imaged in the image information of the area before the branch point; wherein, if there is no lane marking or only a partial lane marking imaged in the area before the branch point, the controller: obtains image information of the branch point including a captured image of a first lane marking; and determines a lane in which the vehicle is traveling after the branch point based on an imaging order of the first lane marking, a form of the first lane marking, a position of the first lane marking in the image information of the branch point, and the road information.