Lambert came through Middlesbrough's youth system,[3][4] before joining Scottish Premiership club Dundee in 2017.[5] He made his professional debut at home to Celtic on 26 December 2017, replacing Faissal El Bakhtaoui after an hour of the 2–0 league defeat,[6][7] and signed a new contract in January 2018.[5] Lambert made five Premiership appearances for Dundee, seven in all first-team competitions,[8] before he was released at the end of the 2018–19 season.[9]
Lambert returned to England and signed for League Two club Scunthorpe United in July 2019, as part of their under-23 side.[10] He joined National League North club Darlington on 15 November on a month's loan,[11] and made his debut the following day as a half-time substitute with his new team already 5–0 down away to Brackley Town.[12] The loan was extended for a second month,[13] and he made eight league appearances before returning to his parent club.[14][15] After a month on loan at another National League North club, Blyth Spartans, during which he made three league starts,[16][14] he returned to Darlington on 6 March 2020 for the rest of the season,[17] but was not used in either of the matches played before the season was curtailed because of the COVID-19 pandemic.[14] He was released by Scunthorpe at the end of the season.[18]
On 7 September 2020, Lambert joined Icelandic 1. deild side ÍBV until the end of the season,[19] but the league was suspended and then abandoned in October because of COVID-19,[20] by which time he had scored once from three matches.[14]
In September 2021, he rejoined Darlington on non-contract terms.[24] On 12 November, after two goals from seven league appearances, he signed a contract with Darlington,[25] and finished the season with eight goals from 35 appearances in all competitions.[14] In 2022–23, he had twelve goals before Christmas, and amid interest from EFL clubs, Darlington were hoping to persuade him to accept another contract;[26][27] he stayed with the club, without a new contract, and finished the season with sixteen goals.[14] On 20 May 2023, Darlington announced that Lambert would leave the club at the end of the season.[28]
Having played little during the early part of the 2024–25 season,[14] Lambert rejoined Darlington on 29 November 2024 on loan until 1 January 2025.[30] He scored once in seven appearances before the loan was extended for a further month.[31]
Career statistics
As of match played 1 January 2025
Appearances and goals by club, season and competition
^Magnússon, Elvar Geir (7 September 2020). "ÍBV fær enskan miðjumann (Staðfest)" [ÍBV get English midfielder (confirmed)]. fotbolti.net (in Icelandic). Retrieved 9 September 2020.
^"Keppni hætt" [Competition stopped] (in Icelandic). Knattspyrnusamband Íslands. 30 October 2020. Retrieved 16 September 2021.