The Reds went unbeaten in the league throughout the month of January with three wins and two draws including a 3-2 victory over Blackburn Rovers, a superb away win at Brentford and a comfortable 3-1 success against Luton Town.
Lamouchi praised the work of his backroom staff after accepting the award.
He said: “January has been a good month for us and we hope to continue that form into February. This award reflects all the hard work my staff and the players have put in. We win, draw and lose as a team so it is important for me to include them as we are all important cogs in the machine.“