At the 2018 CFL combine, Godber was asked to leave after declining to participate in events due to illness.[2] Despite this, he was able to work out at Rice's pro day, where his results would have ranked in the short shuttle, three-cone and bench compared to other lineman if it were done at the combine.[3]
On May 3, 2018, Godber was drafted by the BC Lions on May 3, 2018, with the third overall pick of the 2018 CFL Draft.[4] Godber officially signed with the Lions on May 20, 2018.[5] He played in nine games in his rookie year in 2018 and made his first start on September 14, 2018, against the Montreal Alouettes.[1] Godber suffered a season-ending leg injury on September 29, 2018, against the Hamilton Tiger-Cats, which led to him missing most of the 2019 season.[1] He did not play in 2020 due to the cancellation of the 2020 CFL season.[1]
In 2021, he started in all 14 regular season games for the team at centre.[1] He became a free agent upon the expiry of his contract on February 14, 2023.[6]