The released Manchester United striker is being linked with a return to Anfield.
But Lawro wrote in the Mirror: "For me it is a retrograde step and Liverpool should never have left themselves in a position where they even have to be considering it.
"In terms of being fit and available you have to ask how often that will be the case with Owen.
"I also get the impression with him that it is not just about the fact that he only wants to play football.
"If that was the case then he would have lowered his salary demands and signed for a Championship club.
"I just don't think he wants to play for the love of the game any more."