Lakic, who arrived in Frankfurt on loan from Wolfsburg just prior to the transfer deadline, grabbed a brace in the first half at the HSV Arena as the Eagles extended their advantage over fifth-placed Mainz to six points and denied Hamburg a place in the top six for the first time all season.
Frankfurt completed the double over Hamburg, inflicting their first home defeat after four wins in a row, and boosting their hopes of playing Champions League football next season.
Lakic first popped up in the danger area in the ninth minute, heading just wide of the post from Sebastian Rode's cross.
Hamburg did not heed the warning, though, and continued to allow the former Kaiserslautern and Wolfsburg forward too much room.
He punished them in the 22nd minute when he poked the ball over the line after reaching Stefan Aigner's ball in front of goal.
He scored his and Frankfurt's second in the 36th minute, heading in Aigner's cross after being left unmarked once again by the Hamburg defence.
Not only did the Hamburg rearguard ignore the threat of Lakic, but they also continued to allow Aigner too much space to create further chances.
And then there was Alexander Meier, who found room to hit the outside of the post early in the second half with the Hamburg defence totally overwhelmed.
Rene Adler prevented Meier from scoring in the 57th minute as Frankfurt threatened a third on the counter-attack with the home team taking even more risks by attacking.
As time ran out, Marcus Berg wasted a good chance to set up a grandstand finish before Meier was again denied by Adler in the dying stages.