Lynn Krieger -- the wife of the legendary guitarist of The Doors, Robby Krieger -- is dead ... TMZ has learned.

Sources with direct knowledge tell TMZ ... Lynn died in her sleep Thursday after battling a longtime illness.

We're told paramedics were called to Robby and Lynn's Beverly Hills home just before noon for a possible cardiac arrest, but Lynn was already dead when fire and police personnel arrived.

Law enforcement also received a call for a natural death. Her official cause of death is not known at this time.

Lynn met Robby and the rest of The Doors at a New York City nightclub in 1967. They married in 1972 and had one child together -- a son named Waylon.

She was 79.

RIP