Lawrence was claimed off waivers by the Mariners on Thursday.
To clear room on the 40-man roster, pitcher Evan Scribner was transferred to the 60-day DL. Lawrence owned just a 8.78 ERA through 13.1 innings with the Blue Jays this season before being designated for assignment. He did post a 0.90 ERA through 10 innings with Triple-A Buffalo, though that wasn't enough for the Blue Jays to keep him rostered. He should head to Triple-A Tacoma for the time being.