Lake was sent to minor-league camp Sunday, Greg Johns of MLB.com reports.
Lake signed a minor-league deal with the Mariners on Wednesday, which includes an invitation to spring training, Ryan Divish of The Seattle Times reports.
Lake signed a minor league contract with the Red Sox on Friday, SB Nation's Chris Cotillo reports.
Lake was designated for assignment Tuesday, Blue Jays broadcaster Mike Wilner reports.
Lake's contract was selected by Toronto on Wednesday.
Lake was outrighted to Triple-A Buffalo on Sunday, Shi Dividi of Sportsnet reports.
Lake was designated for assignment Monday.
Lake played in 13 first-half games for this season, going 5-for-19 (.263) with a home run and two doubles while posting a .391 OBP.
Lake went 1-for-3 with a walk and an RBI Wednesday against the Rockies.
Lake was promoted from Triple-A Buffalo on Friday.