Henry Lau made his debut in the 2013 South Korean-Thai drama film ‘Final Recipe’ directed by Gina Kim. The film saw its premiere at the San Sebastián International Film Festival and received mixed reviews from critics. In 2015, he made his television debut in the Korean drama series ‘Persevere, Goo Hae-ra’ where he played the role of ‘Henry.’ The show garnered praise from critics and audience alike. That same year, he also appeared in the South Korean television series ‘Oh My Venus’ directed by Kim Hyung-suk. Lau has also appeared in several reality television shows such as ‘MasterChef Korea Celebrity’ (2013), ‘Always Cantare’ (2014), ‘Real Man’ (2014-2015), ‘We Got Married 4’ (2015), ‘Always Cantare 2’ (2015), ‘Where Is My Friend's Home’ (2015), ‘Sisters Over Flowers 2’ (2016), ‘Back to Field’ (2017), ‘Perhaps Love 4’ (2017-2018), ‘I Live Alone’ (2017-2021), ‘Back to Field 2’ (2018), ‘Super-Vocal’ (2018-2019), and ‘Begin Again 3’ (2019).
In 2019, he starred as ‘Trent’ in the American family comedy-drama film ‘A Dog's Journey’ directed by Gail Mancuso. The film received mixed reviews from critics and was a major box office success, grossing over $75.8 million against a budget of $16 million. The film also marked the Hollywood debut of Lau. That same year, he also made an appearance in the South Korean television series ‘Level Up.’ The following year, he starred as ‘Dong Yilong’ in the fantasy action film ‘Double World’ directed by Teddy Chan. The film received mixed to positive reviews from critics. In 2021, he became a part of the second season of the comedy-drama series ‘Dramaworld’ directed by Chris Martin. He played the role of ‘Woo Sung’ in the series.