The 32-year-old Basel native, who won his only Paris title in 2009, was watched by wife Mirka and older twins Myla and Charlene but not three-week old Lenny and Leo.
Sunday's triumph was also his 59th at Roland Garros, tying eight-time champion Rafael Nadal as the tournament's win specialist.
Federer was never troubled by Lacko, the world number 88 who has not won a clay court match for three years.
Breaks in the fifth and seventh games of the opening set followed by another in the third game of the second put the 17-time major winner in total control.
Federer broke again in the first and fifth games of the third set against the hapless Lacko to seal victory in just 84 minutes, a performance highlighted by 40 winners.
Federer goes on to face either Portugal's Gastao Elias or Diego Sebastian Schwartzman of Argentina for a place in the last 32.
"It was important for me to attack and stay aggressive," said Federer.
"I also served well."
Federer was joined in the second round by big-serving Canadian eighth seed Milos Raonic who unleashed 27 aces in his 6-3, 7-6 (7/1), 6-3 win over teenage Australian wildcard Nick Kyrgios.