Lugo signed a contract Monday with the Guadalajara Mariachis of the Mexican League.
Lugo cleared waivers and was outrighted to the Tigers' alternate training site Saturday.
The Tigers designated Lugo for assignment Monday, Cody Stavenhagen of The Athletic reports.
Lugo is starting at third base and batting seventh in Tuesday's game against the White Sox.
Lugo is a member of the Tigers' 30-man Opening Day roster.
Lugo is a part of the Tigers' 60-man player pool this season, but he's facing competition from Jeimer Candelario, Isaac Paredes and rookie Spencer Torkelson in camp.
Lugo and fellow third baseman Jeimer Candelario could both make the Tigers' Opening Day roster if teams get to keep more than 26 players, Chris McCosky of The Detroit News reports.
Lugo could be waived if he loses the third base competition to Jeimer Candelario, Evan Woodbery of MLive.com reports.
Lugo won't be available for Thursday's Grapefruit League game against the Braves due to back tightness, Chris McCosky of The Detroit News reports.
Lugo is batting just .083 through seven spring training games.