But there were no signs of his recent struggles as he kickstarted his claycourt campaign in style to record a victory over fellow Serb Lajovic in just 57 minutes.
Djokovic, a two-time winner at Monte Carlo, dropped just eight points as he wrapped up the first set with his opponent well off the pace.
Lajovic, ranked 93 in the world, offered resistance in the second set to level at 1-1 but failed to capitalise on a break point as the 12-time grand slam winner roared back to book a second round meeting with Borna Coric of Croatia.
Earlier in the day, Japan's Kei Nishikori came back from a set down to see off Czech 12th seed Tomas Berdych 4-6 6-2 6-1 and reach the second round.
Nishikori, who missed a large part of last season with a wrist injury, started the season in the Challenger Tour events before reaching the second round at Miami.
He was playing close to his best tennis despite calling for a medical timeout for his troublesome wrist.
"It's not great but first match on clay, you know, I'm expecting little soreness," Nishikori said.
"Hopefully I have a day off tomorrow. If I have to play tomorrow, I got to be ready tonight."
The 28-year-old, who is making his first Monte Carlo appearance since 2012, will face Russian Daniil Medvedev in the next round.
World number 51 Jared Donaldson confronted an umpire after disagreeing with a call made in his first-round defeat by last-year's finalist Albert Ramos-Vinolas.
While 6-3 3-2 down, the 21-year-old American became outraged when a serve by the Spaniard was called in by Arnaud Gabas when he believed it was out.
Donaldson eventually lost 6-3 6-3 and apologised to Ramos-Vinolas but refused to shake Gabas' hand.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
