Lambe began his professional career with
Ipswich Town, joining from Bermudian club
Dandy Town Hornets, playing on the youth team and eventually joining the reserve squad, as well as making a first team appearance in a
League Cup match against
Shrewsbury Town. Lambe made his league debut in Ipswich Town's victory over
Middlesbrough at
Riverside Stadium on 7 August 2010, replacing
Carlos Edwards in the 64th minute. The game ended in a 3–1 win for Ipswich Town. Lambe joined
Bristol Rovers on loan on 24 March 2011. While with Rovers Lambe made seven league appearances. Lambe signed with Canadian club
Toronto FC, of
Major League Soccer (MLS), on 7 December 2011. Lambe scored his first goal(s) for Toronto in league play, scoring twice against
Chicago Fire on 21 April, the game ended in a 3–2 home defeat. Lambe helped Toronto win the
2012 Canadian Championship with two goals, tying him with three other players for the Canadian Championship Golden Boot. He was put on waivers by Toronto FC on 5 March 2014. After being waived by Toronto FC, Lambe joined
Nyköpings BIS of Sweden's
Division 1 Norra. Over three months, Lambe made twelve appearances for the club, scoring one goal before leaving. After leaving Nyköping, Lambe had a short trial with
Mansfield Town before officially signing for the club for the
2014–15 season on 17 September 2014. Three days later, Lambe was named to the lineup as a substitute for Mansfield Town's league match against
Carlisle United. Lambe went on to debut for the club in the match, coming on as a 74th-minute substitute for
Fergus Bell. Lambe joined League Two rivals
Carlisle United in June 2016. He scored on his debut in a 1–1 draw with
Portsmouth on 6 August 2016. At the end of the 2017–18 season he was released by Carlisle. On 28 June 2018 Lambe joined League Two club
Cambridge United on a two-year contract. He scored his first goal for Cambridge in a 3–1
EFL Trophy loss to
Southend United on 4 September 2018. In 2020 Lambe signed for
Stowmarket Town. Lambe scored on his debut in a 5–0
FA Vase win over
Eynesbury Rovers. He left to join
AFC Sudbury in February 2023. On 29 June 2023, Lambe agreed to join
National League South side,
Braintree Town following a successful promotion campaign with AFC Sudbury. On 6 May 2024, he scored the winner with a diving header in the second half of extra time as Braintree defeated
Worthing 4–3 to earn promotion to the National League. On 27 September 2024, Lambe joined
National League North side
Needham Market. ==International career==