In June 2023, it was announced that Lawrence would join Surrey on an initial three-year deal ahead of the 2024 season.

In the 2023/2024 season of the Big Bash League (BBL13) Lawrence joined the Melbourne Stars as an international recruit.

[11][12] Lawrence put in a man-of-the-match performance as the England Lions wrapped up a series win against a Cricket Australia XI in February 2020.

[14] A fortnight later, Lawrence's fine form for the Lions continued with an impressive 190 runs and three wickets in a four-day tour match against the same opposition.

[15] On 29 May 2020, Lawrence was named in a 55-man group of players to begin training ahead of international fixtures starting in England following the COVID-19 pandemic.

[16][17] On 17 June 2020, Lawrence was included in England's 30-man squad to start training behind closed doors for the Test series against the West Indies.

[23] He made his international debut in the first Test of this series scoring an impressive 73 in the first innings before being caught at short leg.