The 27-year-old, who left the Shrimps after over 120 appearances across three years to join Rotherham two seasons ago, has signed a one-year deal.
"Lawrence was always an excellent player for us and one of the best left backs in League Two," boss Jim Bentley told the club's official website.
"He left us to join Rotherham and although things didn't quite go to plan for him there, I had no hesitation in bringing him back to the club after his spell at Accrington.
"He is a quality player who is hungry to be successful here. He's fitted back into the club superbly and impressed with his attitude and application during pre season."