Lucas was replaced at half-time after suffering what Atletico described as a "strong facial trauma" in a 1-0 defeat away to Sporting CP, Diego Simeone's men heading through 2-1 on aggregate.
Costa followed shortly after the restart after the striker appeared to sustain an injury to his left leg, but 2010 and 2012 winners Atletico were able to cling on despite a Sporting charge led by Fredy Montero.
Injuries to Costa and Lucas come as a blow to Simeone, who saw his squad options reduced by the sales of Nicolas Gaitan, Augusto Fernandez and Yannick Carrasco - who all moved to the Chinese Super League - during the January transfer window.
Atletico's possible opponents in Friday's semi-final draw are Salzburg, Arsenal and Marseille.
April 12, 2018