The fourth-seeded, 17-time major winner goes on to face either Luxembourg qualifier Gilles Muller or Julien Benneteau of France for a place in the last 32.
Defeat for Lorenzi meant the 32-year-old has still to win a match at a Grand Slam in 11 years and his record at the majors of no wins and 13 losses is the second worst in history.
Federer came into the tournament buoyed by a seventh Halle grasscourt crown last week, but lost to Ukraine's Sergiy Stakhovksy in the second round 12 months ago. That was his earliest defeat at the tournament since 2002.
The Swiss took victory on a sixth match point having fired nine aces and 36 winners.
"It's always good to win the first round because the court can be slippery sometimes," he said.
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