The reigning Australian Open champion raced out of the blocks to break Slovakian Lacko in just the fourth game of the opening set.
The unseeded Lacko was able to trade blows with the Serbian from the baseline and, on occasions, looked to unsettle the No. 2 seed, but whenever Djokovic began to dictate from the back of the court then there was only going to be one winner.
The second set was a much more even affair, with neither player able to break their opponent’s serve as a tie-break was required to separate the two. Lacko was unable to keep pace with Djokovic, winning just two points in the breaker.
The Slovakian looked visibly disheartened during the third stanza and was put to the sword by the relentless Serbian.
"It is the first competitive match I've had this season, I haven't played for five or six weeks," Djokovic said.
"I was a bit rusty on the court the first two sets. Afterwards it was all working well."
The second seed, who was watched by his new co-coach Boris Becker, next faces Argentine Leonardo Mayer, who earlier beat Spain's Albert Montanes 6-1 6-3 6-1.