A product of the club's youth academy, Burge signed his first professional contract with the Sky Blues in the summer of 2011.
During the 2012/13 season, Burge gained valuable first-team experience at Blue Square Premier side Nuneaton Town, making 17 appearances for the Boro.
He kept an incredible 10 clean sheets during his stint, playing a major part in keeping Nuneaton in the league, and signed a new deal with the Sky Blues in 2014 to extend his stay until June 2017.
The next season, Lee made his debut for the first team and was handed the number one shirt, accumulating 18 appearances during the 2014/15 campaign.
Burge continued to battle for a starting position and during the 16/17 season he was able to cement that, featuring in the majority of the Sky Blues games during the relegation from League One to League Two and also helping City to win the Checkatrade Trophy.
Last season, Lee was instrumental in City securing promotion back to League One at the first time of asking. His performances earnt him a place in the EFL League Two Team of the Season.