A man punched a dog that barked at him before attacking its owner on the Promenade in Cleveleys, police said.
The pet's owner, a woman in her 20s, was punched and kicked in the incident, which happened at around 6pm yesterday.
Officers have now released pictures of a man they want to speak to - and appealed for the public's help in finding him.
He was described by PC Potts as in his 50s or 60s, with a podgy, overweight build, around 5ft7in tall, balding, and wearing glasses.
The pictures, understood to have been taken by the victim, show the man with a dog.
One also shows the man, who was wearing a dark jacket and jeans, reaching to pick a pair of glasses up off the ground.
Information can be reported by calling 101, quoting log number LC-20171106-1091.