The midfielder signed an initial one-year contract with Blues in the summer of 2013.
He had spent the previous six weeks at the club on an emergency loan from Barnet.
During that period, the former West Ham United trainee captained Blues U21s in the U21 Professional Development League Two North and made an appearance on the first-team bench for the final 2012/13 npower Championship fixture of the season.
Lee had previously enjoyed loan spells at Dagenham & Redbridge and Gillingham before signing for Barnet in the summer of 2012.
He made his first team bow for Blues in the Capital One Cup victory against Plymouth in August 2013 and in total made 20 appearances during his debut season for the club.
Lee signed a new one-year deal in the summer of 2014.