Lima scored the only goal of the game shortly after half time to give the Portuguese league leaders an important win.
After an even start the hosts started to put pressure on Benfica with a series of dangerous free kicks.
The Portuguese side were able to hold out, despite a couple of penalty appeals, and set about finding a meaningful attack of their own, primarily through their full-backs.
It was their left-back Silvio who went closest, wriggling free towards the end of the half, but firing over from outside the box.
Benfica started the second half much more purposefully and their pressure told after just 15 minutes when a questionable offside call allowed Lima to find space in the box and smash the ball past the goalkeeper.
The hosts pushed forward after that and almost allowed Benfica to get a second late on when Lazar Markovic broke free on the counter-attack, but his effort was saved by Panayiotis Glykos to keep the score at one going into next week's return leg.