Cosart will make his Marlins debut on Friday.
To make room for one of the players on the 40-man roster, the Marlins are expected to designate left-hander Donnie Joseph for assignment. Joseph was acquired from the Royals on June 30 in exchange for cash considerations when the team was struggling to find pieces for their bullpen.
Jennings allowed all three of his inherited runners to score in his sixth-inning appearance against the Nationals on Monday. He gave up a hit and issued a walk in a scoreless ninth inning on Wednesday.
In 35 games with the Marlins this year, 11 of the 20 runners Jennings inherited have come in to score.
Lucas was recalled from New Orleans before Wednesday's game, but did not make an appearance.
Maria Torres is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.