She was identified Tuesday as Laurel A. Moody, 61, according to the Snohomish County Medical Examiner's Office.
Moody died of smoke inhalation. Her death was ruled an accident.
The fire was reported about 6 p.m. at Gateway Apartments along 240th Street SW. The fire was contained to Moody's apartment in the six-unit complex.
Crews found her body inside. Her cat also died in the fire.
People who live in the apartment complex were allowed to return to their homes at about 11:30 p.m. Monday.
The lamp was the clip-on kind used on a shelf or headboard, said Leslie Hynes, spokeswoman for Snohomish County Fire District 1.
"It appears the lamp came loose and landed on the victim's bed in the living room," Hynes said.
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