ST. PETERSBURG, Fla.—The parents of Gabby Petito claim in a new Florida lawsuit that Brian Laundrie told his parents he had killed her before he returned home alone from their ill-fated western trip in a converted van. The lawsuit filed Thursday in Sarasota County Circuit Court contends that Laundrie told his parents on Aug. 28 that he had killed Petito, 22, his fiancee of about a year at the time. Petito’s disappearance on the trip and the subsequent discovery of her slain body Sept. 19 in a Wyoming national park became a national obsession, augmented by the later search for Laundrie in a Florida nature preserve. The FBI concluded that Laundrie strangled Petito—with whom he had previous domestic quarrels and violence—and that Laundrie fatally shot himself in the Carlton Reserve swamp after returning home alone Sept. 1. The lawsuit contends that Christopher and Roberta Laundrie concealed that their son had …