The 17-year-old left-hander from Worthing overcame the challenge of another big-server, Peter Wessels of the Netherlands, 6-3, 7-6 to earn a match with the third seed, the Mexican Alejandro Hernandez.
Lee, an admirer of Goran Ivanisevic, showed a resemblance to the Croatian player as he served 11 aces and demonstrated courage and determination to come back from 0-4 down in the tie break.
"I'd played the guy four times before and never beaten him so I was very pleased with my game," Lee said. "His game is suited to grass and I'm very happy to have won."
Lee's aggressive style - hitting the ball hard on both wings and using a double-handed backhand - is matched by a fierce will to win and self- criticism, demonstrated on the rare occasions when he played false shots.
"I know how well I can play and 90 per cent of the time today I played the way I wanted to," he said. "I could have done better on a few shots but I'm very confident on grass because of my serve."
Lee and his partner, James Trotman, are already in the second round of the doubles. But another British pair, Warwickshire's Jamie Delgado and Kent's Alex Osterrieth, failed to reach that stage when they were beaten 3-6, 7-5, 6-2 by the third seeds, Germany's Tommy Haas and the American, Greg Hill.Reuse content