Red Star reach Serbian Cup final
Holders Partizan Belgrade and Vojvodina Novi Sad meet in the other semi-final on Thursday.
Red Star, who are four points clear of Partizan at the top of the first division, produced a below-par peformance on a rainy evening but an opportunist strike from Lekic kept them on course to wrestle the domestic double from their city foes.
OFK Belgrade goalkeeper Bojan Saranov pulled off a string of fine saves to keep his side in the match but could do nothing in the 87th minute, when a hesitant half-clearance fell kindly for Lekic to steer it home from seven metres.
OFK had defender Sasa Markovic sent off for a second yellow card shortly after the hour, having been booked for a foul in the first half before he handled a dangerous cross from the right.