Number one seed Djokovic took the first set with a 6-2 victory.
The Serbian stepped up to another level in the second set, winning it 6-0.
Lorenzi battled hard to try to stop Djokovic's rhythm, earning the respect from the fans in the court. However, the gulf in class was too wide and Djokovic took the final set 6-0 to win the game.
Djokovic now heads into the second round.