The Jets cut Doctson on May 7. He signed with the Jets in 2020 before opting out of the season over COVID-19 concerns.
Doctson, 28, entered the league as a first-round pick of Washington in 2016. He played only 33 games with 26 starts in his career there before moving on to the Vikings, where he appeared in one game.
In his career, Doctson has 81 catches for 1,100 yards and eight touchdowns.
Lewerke, 24, is a former Michigan State quarterback.
He went undrafted in 2020, signing with the Patriots as a free agent. Lewerke spent some time in the Patriots’ training camp last summer.
Lewerke signed with the Alphas of The Spring League in May.