Total rainfall of nearly one metre was expected on the higher windward slopes, turning rivers into raging torrents and threatening mudslides.
Tropical storm conditions were spreading westward on Sunday from Maui to Oahu and then Kauai, and the National Hurricane Centre warned that wind speeds atop mountains and on the windward and leeward slopes are often up to 30 per cent stronger than the near-surface winds used to categorise storms.
Powerful waves pounded the Big Island's coast as Lala slowly passed by. Howling winds whipped palm trees and waterways swelled with fast-moving runoff from relentless rain that blew nearly sideways.
More than 130,000 households were without power on Sunday morning across Hawaii's three largest islands, according to the utility tracker US Power Outage Map. At least three hospitals were operating on generator power, Governor Josh Green said.
At least one person died in a car accident in the South Point area of the Big Island, while 19 roofs were lost in the "enormous storm," the governor said.
"There have been a lot of roads impacted; our crews have already been out to more than 30 sites."
A search-and-rescue mission including Civil Defence, the National Guard and Coast Guard was launched after flash floods apparently swept several occupied homes off their foundations in the coastal communities of Na'alehu and Wai'ohinu, near the island's southern tip, Hawaii County Mayor Kimo Alameda said early on Sunday.
"What makes this very challenging is that there's rushing water, there's debris, and there's boulders on the road and it's dark," Alameda said.
Tropical storm warnings were in effect for the islands of Maui, Molokai, Lanai, Kahoolawe, Oahu, Kauai and Niihau as the storm moved west, raising the possibility of destructive flooding and even wildfires kicked up by strong winds.
Early on Sunday morning in Hawaii, Lala was centred about 170 km west-northwest of Kailua-Kona and about 160km south of Honolulu, with tropical-storm-force winds extending as much as 280 km from its centre.
Lala was sustaining top winds of 110km/h and moving northwest at about 24km/h.
Forecasters expect it to regain hurricane strength midweek once it's well west of the island chain.
By the time Lala's completely gone, some higher-altitude places on the Big Island, dominated by the towering Mauna Kea volcano, will have been hit with as much as 89cm of rain, forecasters said, enough to loosen steep slopes where some of the 210,000 islanders live off the grid in improvised housing.
As the hurricane approached, shelters were opened, events were cancelled and ranchers were urged to leave their cattle in pastures rather than structures that might collapse.
Many residents are still dealing with the aftermath of devastating floods in March and were taking precautions.
Bobby Camara, a 75-year-old lifelong resident, said he planned to "hunker down, cross my fingers, hope the lights don't go out" at a care home just outside Hilo. He said petrol stations were busy as people sought fuel for chainsaws and vehicles.
"I think stocking up is part of life over here. ... You learn to be self-reliant," Camara said.
Christine Matsuda, who lives in Waimea, on the northern side of the island, said "big gusts every few minutes rattle the whole house".
"We're finding unexpected leaks in places that don't see water under normal conditions," Matsuda said.
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