Lee came to Manchester United as a junior player in 2002. In 2005, he helped United's reserve team win the quadruple. In the 2005–06 season he was loaned to Macclesfield Town for what was originally going to be a month, but was extended to three months.
Lee made his league debut away at Oxford United. During his loan period, Macclesfield boss Brian Horton told the Macclesfield Express: "Tommy has been excellent since joining us in January. I spoke to Tony Coton, United's goalkeeping coach, and Sir Alex Ferguson. Both were happy to extend Tommy's loan spell."
In August 2006, he signed a contract with Macclesfield, arriving on a free transfer from Manchester United.
On 6 January, 2007, Lee kept goal for Macclesfield Town against English Champions Chelsea at Stamford Bridge. Despite suffering an injury to his arm on a save from Chelsea striker Salomon Kalou, he continued to keep until he was awarded a Red Card and subsequently sent off after a foul on Chelsea striker Andriy Shevchenko. This sending off reduced Macclesfield to 10 men and signalled the beginning of the 6–1 rout of Macclesfield by the Premier League Champions.
On 22 March, 2008, Lee joined Rochdale on loan from Macclesfield Town and played in Rochdale's Play Off Final appearance at Wembley Stadium against Stockport County. Lee was released by Macclesfield in May 2008, before joining Chesterfield on 1 August on a one year contract.
In September 2008, Lee was attacked during a night out in Sheffield. He required surgery after he broke his jaw during the attack, and is expected to be out of action for six weeks.