Authorities said Lake was trying to refuel a portable heater when a couch caught fire.
She and her two sons, ages 9 and 13, evacuated quickly and were standing outside the rented home when the first fire truck rolled up.
The home, in the 18900 block of PCH, suffered extensive damage in the fire, which broke out at 7:28 a.m.
The first firefighters on the scene put hoses down from the highway onto the beach and sprayed water up into the structure's wooden piers, witnesses said.
Flames rose 30 feet on the air as the attic and roof burned. Firefighters used power tools to cut into gates at adjacent houses to protect them.
PCH was closed in both directions about 1/2 mile northwest of Topanga Beach, and motorists were told the state highway would be blocked for two hours.
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