'Mystery Man'
In the trivia section it says Lynch revealed in 2002 that Lost Highway takes place in the same universe as Twin Peaks.
To me, the Mystery Man is obviously supposed to be a Black Lodge being. Either a projection from Fred's own mind, to distance himself from his crimes, or simply a personification of the evil inside him. This personification could be a real entity, if we go the TP route. But it all points to the same conclusion: he's inhabiting Fred, is responsible for the murders, and is the reason Fred cannot remember what exactly has happened.
In my opinion, it's entirely possible that Fred is "reliving" his experiences, from the very first frame of the film, from the place beyond the Black Lodge.
(And remember, the Black Lodge was always metaphorical- but it had mystical qualities that were fleshed out in Twin Peaks.)
"Sorry detective. There was a fish... IN the percolator."