"When the going gets tough, the tough gets going. Joshua proved that and really wanted it. It showed his fitness was great as well," said Lewis, who won super-heavyweight gold at Seoul 1988.
"In four years [since he started boxing] he has achieved so much. Heavyweights are known to mature later so it's a great achievement to beat an Olympian of excellence and a world champion.
"He can either stay amateur or go pro but he has a great future ahead of him."
Meanwhile, Joshua has expressed his desire to remain in the amateur game in order to compete at Rio 2016.