Granados and Lagos scored within 18 minutes of each other after a goalless first half at Estadio Eladio Rosabal Cordero to complete a 3-1 aggregate victory for Herediano.
Herediano - contesting their first Champions League semi-final having failed to make it past the quarters in four previous attempts - will face Mexican heavyweights America for a spot in the final.
Hosts Herediano held the upper hand heading into Thursday's return leg after claiming a 1-1 draw in Honduras last week.
But Olimpia almost regained the ascendency when they were awarded a penalty in the 30th minute but Honduras international Anthony Lozano was unable to convert.
And the visiting team were left to rue their missed opportunity as Herediano scored two unanswered goals after the break.
Granados put Herediano ahead on aggregate just a minute into the second half before Lagos, who netted the equaliser in the opening leg, tucked the ball underneath Olimpia's international goalkeeper Noel Valladares.
