Caroline Stead, 59, tragically died after being involved in a collision with a silver BMW in Brighton Road at around 7.20am, police said.
Her family have paid tribute to their mother, daughter and sister, who was crossing the road with her dog at the time of the accident.
The tribute read: “Caroline Victoria Stead, mother, daughter and sister, passed away in a fatal accident earlier this week at the age of 59. She was a warm and outgoing person who easily made friends. Born in Kilmacolm, Scotland, she had the fortune to travel widely in her youth.
"A celebrated cook and loving mother, her youthful and bubbly spirit will be dearly missed by friends and family. She leaves behind a loving family who will not be making further comment.”
Emergency services, including an air ambulance, were sent to Beach Green in Lancing on Monday in response to the incident.
Sussex Police said Caroline had been crossing the road with her dog when she was in a collision with a silver BMW being driven by a 47-year-old man from Shoreham. Sadly, she died at the scene.
Her dog ran off, police said, but was found a short while later and taken to a vet for treatment for a paw injury.
Police are trying to establish the circumstances of the incident and would like to hear from anyone who witnessed the collision or who may have dash cam footage as they were passing. Please email [email protected] or call 101 quoting Operation Desk.