The Rays acquired Lesko, outfielder Homer Bush and catcher J.D. Gonzalez from the Padres on Sunday in exchange for reliever Jason Adam, Joel Sherman of the New York Post reports.
Lesko was one of San Diego's top prospects, though he's struggled at the High-A level this season with a 6.82 ERA, 1.59 WHIP and 73:49 K:BB across 64.2 innings. He's also plunked 11 batters and thrown seven wild pitches, as his control has been erratic in his second year back from Tommy John surgery.