The incident took place in the Mareham le Fen area last Tuesday lunchtime (August 1).
According to police, the dog was in a grey Ford Ranger which was later abandoned.
Police stress the dog was not hurt.
The vehicle was found dumped by the roadside between Coningsby and Kirkby on Bain.
Police are also seeking information about the theft of a vehicle from a farm in the Bucknall area last Monday night.
A Green Land Rover Defender 110 was stolen between 9pm and 8am.
Anyone with information is asked to call 101 or Crime Stoppers 0800 555 111.