The long-running debate over dogs on Lambert’s Cove Beach isn’t over yet.

West Tisbury voters, who agreed three weeks ago at their annual town meeting to let residents walk their dogs on the beach on summer mornings, are being asked back to a special town meeting on June 5 to decide whether they want to pay to enforce good behavior by owners and their pets. The warrant is expected to ask voters to back funding for a seasonal assistant animal control officer to patrol the beach, as well as to consider bylaw changes addressing leashes and litter.