The fourth-seeded Federer served nine aces, saved all five break points against him and broke Lorenzi six times.
The only suspense came near the end of the match when Lorenzi saved five match points while serving at 2-5 in a game that went to eight deuces. Federer held serve in the next game, finishing the match with an ace.
"I thought I played very well, served well, played the transition game, came to the net," Federer said. "You want to be eager to play, motivated, not wanting to underestimate anybody and win the tournament and that's why I'm here."
Federer and Lorenzi are both 32, but that's where the similarities end. For the Italian, the loss extended his career Grand Slam record to 0-13. Only one player, Juan-Antonio Marin of Costa Rica, has a worse record, with no wins and 17 losses.
Earlier, Jo-Wilfried Tsonga needed just four points and two minutes to advance and Stan Wawrinka swept through in straight sets.
Tsonga, the 14th-seeded Frenchman, had been set to serve for the match at 5-4 in the fifth set against Austria's Jurgen Melzer when rain forced a suspension of the first-round match Monday.
Tsonga, a two-time semifinalist at Wimbledon, came back out onto Court 1 on Tuesday afternoon and barely broke a sweat. He held serve at love and finished with his 20th ace to complete a 6-1, 3-6, 3-6, 6-2, 6-4 victory.
Tsonga spent more time signing autographs after the match than he did on court Tuesday against Melzer.
"It was tough yesterday," Tsonga said. "Today I just came for one game, but I'm happy to go through."
Australian Open champion Wawrinka, meanwhile, served 18 aces and cruised to a 6-3, 6-4, 6-3 win over Joao Sousa of Portugal.
The fifth-seeded Swiss player was coming off a first-round loss at the French Open in his first Grand Slam since winning his first major at Melbourne in January. It was also Wawrinka's first win since 2011 at the All England Club, where he had lost in the opening round the past two years.
Normally, the reigning women's champion would play the day's opening match on Centre Court. But Marion Bartoli retired shortly after winning last year's title, leaving the honor to runner-up Sabine Lisicki.
The 19th-seeded German fared much better in her return to Centre Court, needing just 57 minutes to put away Julia Glushko of Israel 6-2, 6-1. As if she needed any help, Lisicki benefited from a net cord on the final point, holding up her arms in apology but also smiling in victory.
"Such a huge honor to play out there in the first match today," Lisicki said. "It is such a special place for me."
Before the match, Bartoli returned to Centre Court, wiping away tears during a tribute to Elena Baltacha, the British player who died of liver cancer on May 4 at the age of 30. Wearing her Wimbledon member's tag on her white dress, Bartoli was accompanied by 9-year-old Elle Robus-Miller, a player from the Elena Baltacha Academy of Tennis for underprivileged children.
"I think it was a very, very special moment," Lisicki said.
Two-time champion Rafael Nadal was scheduled to play on Centre Court against Martin Klizan. In women's play, top-seeded and five-time champion Serena Williams was due to play Anna Tatishvili following the Nadal match.
Early women's winners included No. 4 Agnieszka Radwanska, who completed a 6-2, 6-1 victory over Andreea Mitu of Romania. Radwanska led 4-2 when rain stopped play Monday.
Caroline Wozniacki reeled off four consecutive games to complete a 6-3, 6-0 win over Israel's Shahar Peer in another rain-suspended match. The 16th-seeded Wozniacki lost in the first round at the French Open a week after her engagement to two-time major golf champion Rory McIlroy was called off.
Among the men, No. 10 Kei Nishikori was a straight-set winner over Kenny de Schepper.
Follow Stephen Wilson on Twitter: http://twitter.com/stevewilsonap