The defending champion won 6-4, 6-4, 6-1 in one hour, 29 minutes and barely broke a sweat, despite Lacko doing relatively little wrong.
"But, sure, I was also surprised it was that fast, that first set, especially 16 minutes".
Lajovic shook off his early nerves to at least give Federer some practice in the second and third sets but the Serbian could do no better than past year when he also suffered a straight-sets defeat by the Swiss, that time in the second round.
Asked if he expected more from an opponent in the world's top 30, Federer said: "I think it's a tough matchup for him maybe against me". "It really messed with me for two balls, then I tried to just calm down, to play my game".
But Federer offered a contrasting view in his media conference following a 6-0 7-5 6-4 fourth-round win over Adrian Mannarino on Monday.
Bertens and Pliskova had reached the fourth round at Wimbledon for the first time.
Federer's performance was reassuringly familiar, though, as he displayed his typical panache and class with some cute drop shots and trademark backhand slice.
Monday's win took Nadal, 32, into a 35th Grand Slam quarter-final. His decision to skip the French Open this year, for instance, helped him keep his legs for Wimbledon.
The top-ranked Spaniard beat Jiri Vesely 6-3 6-3 6-4 on Centre Court to return to the last eight for the first time since he was runner-up to Novak Djokovic in 2011.
Top-ranked Rafael Nadal is also back in the quarterfinals for the first time since 2011.
The world No.1 will meet either fifth seed Juan Martin del Potro or Frenchman Gilles Simon, whose match was suspended due to darkness with the Argentine leading 7-6 (7-1) 7-6 (7-5) 5-7. The 6ft 10in American served a world-record 113 aces in his remarkable marathon against Nicolas Mahut in 2010, when he won 70-68 in the final set, and has fired down exactly that number over three matches this year. I served well when I needed to. Given how effortless he contrives to make the sport look, it boggles the mind that some questioned whether he would even last until the 2012 Games.
Three-time champion Djokovic, seeded 12, will next face Japan's 24th seed Kei Nishikori.
Since seeds were introduced in the 1920s, it's the first time none of the top 10 women have reached the quarterfinals at Wimbledon.
Former Wimbledon finalist Agnieszka Radwanska lost 7-5, 6-4 to Czech world number 66 Lucie Safarova.
"I guess it was like a huge reveal, wasn't it?" said Mick Desmond, the commercial and media director for the All England Club.
In the Round of 64, while cruising to 6-4, 6-4, 6-1 win over Lukas Lacko, Federer appeared to show off some of the different ways to win points to which he alluded.
The Latvian player also reached the quarterfinals previous year in her best Wimbledon showing, losing to eventual runner-up Venus Williams.
"It's always like a big war for me when I play Novak".
Karolina Pliskova advanced to the third round of Wimbledon for the first time with a 6-3, 6-3 victory over Victoria Azarenka.