The 28-year-old took Federer to a first-set tie-break in 2017 but a hold in the opening game of the match was as good as it got in the early stages.
A post-match interviewer pointed out that Federer could expect more requests from in coming matches after fulfilling her wishes.
The 20-time Grand Slam champion has ended his career-long association with Nike in favour of a deal with the Japanese brand, which is reportedly worth US$300 million and is set to last ten years.
But everything else was familiar for the Swiss star who cruised past world number 57 Lajovic in just 79 minutes.
Federer played at 65 successive slams from the 2000 Australian Open, until missing the French Open in 2016.
After breaking serve twice, the 22-year-old Croat needed only one set point and 25 minutes to wrap up the first set.
Roger Federer and Serena Williams bring the curtain up on Wimbledon yesterday with the All England Club confident their tournament can comfortably capture the imagination of a public distracted by the World Cup.
But Nadal warned organisers at the All England club the move would risk harming the sport and that all the historic matches require extra time between points.
Samsung phones may be sending pictures to random people
We encourage any customers who may have questions or concerns to contact their local Customer Service center at 1-800-SAMSUNG". Multiple people stated there was no evidence on their phone of the error, they only learned of it when the recipient told them.
She next faces either Bulgarian qualifier Viktoriya Tomova or Czech wild card Tereza Smitkova.
"And I think that emphasises the point of how good they've been to stay at the top of the game and obviously win so much in the past decade".
"They know I play a lot of tennis, but they won't know what my ranking would be", Federer told a news conference. "Life goes on", said Stephens, who was followed out of the tournament by Bulgarian sixth seed Grigor Dimitrov.
In the women's event, there were wins for Czech seventh seed Karolína Pliskova who defeated Britain's Harriet Dart 7-6 (7/2), 2-6, 6-1 and 10th seeded American Madison Keys, a 6-4, 6-2 victor over Ajla Tomljanovic of Australia. Sam Querrey, who lost to Cilic in the semifinals a year ago, had a similarly comfortable start as he beat Jordan Thompson of Australia 6-2, 6-4, 6-3.
"It's a great feeling to be back", Williams added.
Wozniacki took 59 minutes to complete the victory on Center Court, finishing it off with a service victor. Past year he reached the fourth round, losing in five sets to Gilles Muller.
The tennis legend was ranked seventh on Forbes' World's Highest Paid Athletes 2018.
Wozniacki breezed past Varavara Lepchenko 6-0, 6-3, Pliskova defeated Harriet Dart 7-6 (7/2), 2-6, 6-1 and Williams won 6-7 (3/7), 6-2, 6-2 against Johanna Larsson.