According to Sydney and Tony, Captain Cook's men massacred the locals and stole the idol of Lono. The locals stole a small boat from Cook, and fought his men on the beach, forcing him to retreat. This is when Cook got killed and his body claimed by the Hawaiians. No idol of Lono was stolen.
According to Tony, Captain Cook's ship, the HMS Resolution, sailed for London in December 1779. Cook was killed in February 1779, after which the Resolution and the Discovery unsuccessfully attempted to pass through the Bering Strait and returned to Petropavlovsk, Russia, where Cook's successor then died on 22 August 1779. The ships did not return home until October 1780.