Rainfall reached a total of nearly one metre in places and sent raging torrents down mountainsides.
A search-and-rescue mission including Civil Defence, the National Guard and a Coast Guard helicopter 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 Big Island's southern tip, authorities said.
"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," Hawaii County Mayor Kimo Alameda said early on Sunday.
At least one person died in a car wreck in the South Point area of the Big Island, Governor Josh Green said on Saturday.
Honolulu was bearing the brunt of Sunday morning's extreme weather as tropical storm conditions spread westward across the island chain.
Honolulu Fire Department had responded to dozens of callouts by 2am local time Sunday, including 58 reports of downed trees, 39 blown roofs, 12 downed power lines, 12 arcing-wire situations and one swimmer rescue, according to a statement from the city.
Much of the state remained under a flash flood warning, though the Big Island was downgraded to a flood advisory on Sunday, according to the National Weather Service.
Heavy rain, mudslides, downed trees, active flooding and downed power lines were among the biggest threats, weather service meteorologist Stephen Parker said.
"Basically, the best thing to do right now is just stay home for a bit longer," he said.
"The storm won't last forever and once those kind of threats get cleaned up, it will be safe to be out and about again."
Fewer than 60,000 homes and businesses were without power by 9:30am local time, down from more than 200,000 just a few hours earlier, according to the utility tracker US Power Outage Map.
At least three hospitals were operating on generator power, the governor said.
Powerful waves pounded the Big Island's coast as Lala slowly passed by.
Just missing landfall, the eyewall didn't weaken, and its winds pounded the mountainsides.
Waterways swelled with fast-moving runoff as bands of rain blew nearly sideways.
Forecasters expect Lala to regain hurricane strength midweek once it's well west of the island chain.
Many residents are still dealing with the aftermath of devastating floods in March and were taking precautions.
Kate McLellan, a resident on Oahu's North Shore, was still waiting for the worst of the storm to strike after her power went out on Sunday morning.
She was glued to the weather network, monitoring Lala's progress.
In March and April, her community was hit by back-to-back storms that moved slowly, leading to a couple of weeks of heavy rain and high winds that kept residents on high alert.
Memories of that storm were "giving that same uncertainty and hesitation and panic and anxiety," McLellan said.
