The world number three was the top seed for this week's tournament after arriving in the Netherlands following his run to the Australian Open final but was dumped out in just over 90 minutes by Serbian Lajovic, currently ranked 27th.
The 20-time Grand Slam champion was due to be playing in Rotterdam for the first time since 2009.
Marseille Open: Stefanos Tsitsipas beats Felix Auger-Aliassime in straight sets to clinch second consecutive title
Although Auger-Aliassime asked tough questions of Tsitsipas in the opening set, coming up to the net to dictate play, the Greek soon started finding his angles to negate that strategy with passing shots
Rotterdam Open 2020: Defending champion Gael Monfils beats Dan Evans in straight sets to advance to semi-finals
Monfils will meet Serb Filip Krajinovic or Russian seventh seed Andrey Rublev, while Spain’s Pablo Carreno Busta faces Canadian teenager Felix Auger-Aliassime in the other semi-final
Rotterdam Open 2020: Rohan Bopanna-Denis Shapovalov pair book semi-final spot with win over Jean-Julien Rojer and Horia Tecau
India's Rohan Bopanna and his Canadian partner Denis Shapovalov advanced to the men's doubles semifinals of the ABN Amro World Tennis Tournament with an impressive win over fourth seeds Jean-Julien Rojer and Horia Tecau.
Rotterdam Open 2020: Vasek Pospisil stuns World No 5 Daniil Medvedev in 1st round; Gael Monfils begins title defence with easy win
Pospisil, who continues a fine run of form having reached the final at the Open Sud de France in Montpellier last week, managed to save five of six break points while converting three of his own en route to a huge upset.
Rotterdam Open 2020: Rohan Bopanna-Denis Shapovalov reach quarter-finals with hard-fought win over John Peers, Michael Venus
Bopanna and Shapovalov will next face the fourth-seeded pair of Jean-Julien Rojer and Horia Tecau on Thursday.
Rotterdam Open 2020: Grigor Dimitrov ousts Denis Shapovalov to reach last 16; Bautista Agut, Pablo Carreno Busta set up all-Spanish clash
Dimitrov admitted he never hit top gear but that did not stop him from setting up a last 16 meeting with either Canadian Felix Auger-Aliassime and Germany’s Jan-Lennard Struff.
Monfils now has one of the biggest titles of his career. You can’t argue against results, even if they come about through seemingly counterintuitive methods.
Rotterdam Open 2019: Gael Monfils overcomes Stan Wawrinka's second-set surge to clinch eighth title of career
Monfils, 32, showed no hard evidence of the left wrist injury which has bothered him all week and forced him onto a regime of pain-killers.
Rotterdam Open: Stan Wawrinka stuns top seed Kei Nishikori in three sets to enter final against Gael Monfils
Three-time Grand Slam title winner Stan Wawrinka reached his second Rotterdam Open final on Saturday by knocking out top seed Kei Nishikori 6-2, 4-6, 6-4.
Rotterdam Open: Kei Nishikori produces near-perfect performance against Marton Fucsovics to set up Stan Wawrinka semi-final
Kei Nishikori continued his unbeaten debut week at the Rotterdam Open with a 6-3, 6-2 defeat of Hungary's Marton Fucsovics on Friday to reach the semi-finals on the back of a performance he described as "almost perfect".
Rotterdam Open: Russian fifth-seed Daniil Medvedev ends Jo-Wilfried Tsonga's seven match win streak to enter semi-final
Daniil Medvedev outlasted 33-year-old Jo-Wilfried Tsonga in a 90-minute struggle to reach the semi-finals and a meeting with Gael Monfils in the Rotterdam Open.
Japan's Kei Nishikori carved out a comfortable 6-1, 6-4 win over Latvian Ernests Gulbis on Thursday to power into the Rotterdam Open quarter-finals.
Rotterdam Open: Jo-Wilfried Tsonga secures straight sets victory over Tallon Griekspoor to set up Daniil Medvedev clash
Tsonga's 7-6 (7/5), 6-1 victory was a match of two parts, with the labourious first set taking 53 minutes while the second lasted for just 23
Rotterdam Open: Top seed Kei Nishikori battles past Pierre-Hugues Herbert; Milos Raonic, Denis Shapovalov advance
Top seed Kei Nishikori was tested by a stubborn opponent before finally putting away Pierre-Hugues Herbert 3-6, 6-1, 6-4 on Tuesday at the Rotterdam Open.
Rotterdam Open: Stan Wawrinka benefits from Benoit Paire collapse to carve out victory in tricky opener
Stan Wawrinka benefitted from a Benoit Paire collapse, with the Swiss carving out a 7-6(7/4), 6-1 win on Monday at the Rotterdam Open
Indian Wells Masters: Roger Federer strolls past Jeremy Chardy to set up rematch with Chung Hyeon in quarter-finals
World No 1 Roger Federer's remarkable run continued as he booked his quarter-final berth in the ATP Indian Wells Masters with a 7-5, 6-4 win over Jeremy Chardy on Wednesday.
The 36-year-old Swiss marvel continues to defy the ageing process, claiming a sixth Australian Open crown two months ago.
Rotterdam Open: Roger Federer calls 97th title-winning week as the best of his life as he returns to World No 1
"It's unbelievable to be number one again after all these (six) years -- this is one of the best weeks of my life," Federer said after winning the final.