Lammers joined PSV Eindhoven's youth system in 2010, having previously played youth football for VOAB and Willem II.[3][4] He signed a three-year professional contract with PSV in July 2015.[5] Lammers made his debut in professional football on 10 August 2015, when he faced Go Ahead Eagles with Jong PSV.[citation needed] On 8 August 2016, he scored a hat-trick in Jong PSV's 5–4 win against Den Bosch.[4]
Lammers made his first-team debut for PSV on 21 September 2016, in a KNVB Cup match against Roda.[6]
In September 2020, Lammers joined Serie A club Atalanta. The transfer fee paid to PSV was reported as €9 million plus €2 million in possible bonuses.[7] On 4 October, he scored his first goal in a 5–2 win against Cagliari.[8]
On 7 August 2022, Lammers joined Serie A club Empoli on a season-long loan.[11] In January 2023, this loan was terminated and Lammers joined Sampdoria on loan until the end of the season.[12]
Rangers
On 15 June 2023, Lammers joined Scottish Premiership side Rangers for an undisclosed fee.[13] He made his debut for the club on 5 August 2023, starting in a 1–0 defeat away to Kilmarnock.[14] He scored his first goal for Rangers during a league match at home to Livingston on 12 August 2023.[15] Lammers scored against Dundee in an away match in November 2023.[16]
On 10 January 2024, Lammers joined Eredivisie club Utrecht on loan until the end of the season.[17] Lammers scored his first goal for Utrecht in a five nil win over Sittard. Following this Lammers went on an unprecedented run of form by scoring in seven consecutive matches for Utrecht which is a club record in the Eredivisie. During this goal scoring run this included a double in an away match against Heerenveen. Lammers finished his loan spell at Utrecht with further goals against Alkmaar and Rotterdam taking his total for the loan spell to eleven goals in twenty matches for the dutch side.[18]
Twente
On 26 July 2024, Lammers joined Twente on a three-year contract.[19]