The cable trapped crew members beneath it killing five of them, officials said.
None of the hundreds of passengers aboard the British-operated vessel were involved in the accident, which also injured three crew members, said the Canary Islands port authority.
Divers raced to the lifeboat, which had hit the water upside down, recovering four bodies and trying without success to revive a fifth crewman who had stopped breathing, the authority said.
Thomson Cruises confirmed the accident and the casualties aboard its Thomson Majesty ship on the island of La Palma, saying the three injured crewmen were not badly hurt.
The ship docked at the island's port of Santa Cruz in the morning, after arriving there from the neighboring island of Las Palmas de Gran Canaria. It was due to depart at 3 p.m. for Funchal on the mid-Atlantic island of Madeira with 1,498 passengers and 594 crew aboard, the authority said.
At 10:30 a.m. a drill consisting of lowering a lifeboat with crew members aboard began.
About an hour later, when the lifeboat was being hoisted back up to the deck, a cable holding it snapped and a hook holding the lifeboat on a second cable gave way, sending the lifeboat plunging into the port upside down, the authority said in a statement.
An alarm was sounded and port authorities were alerted. The captain of the cruise ship called for the divers who arrived at the capsized lifeboat.
The dead crewmen included three Indonesians, a Filipino and a Ghanian, authorities said. The three injured crew members were taken by ambulance to a hospital in La Palma and the nationality of only one of them was immediately known: Greek.
Local authorities of La Palma canceled Carnival festivities that had been due to be held on the island Sunday, but said they would go ahead as planned on Monday.