Detroit released Smith two days ago to activate punter Sam Martin from the reserve/non-football injury list. The Lions signed him two weeks ago to add depth to the defensive line.
The Dolphins originally signed Smith as an undrafted free agent in 2012. He had brief stints with the Jets and Bills before the Buccaneers claimed him in 2014.
Smith, 27, appeared in one game for the Bucs this season but did not record any statistics. They cut him Oct. 5.
He appeared in 29 games with the Bucs, with 18 starts, and he made 13.5 sacks.
Lelito appeared in two games for the Lions, including Sunday night against the Steelers, but he injured his thigh.