The 26-year-old Lu of Taiwan won 4-6, 7-6 (3), 7-6 (4), 6-7 (5), 9-7 on Monday to reach the quarterfinals.
Lu converted his only break point in the final set to secure the victory over Roddick in four hours and 36 minutes.
Lu had previously never advanced beyond the second round at Wimbledon or the third round in any Grand Slam. He becomes the first Asian man to reach the quarterfinals of a Grand Slam since Japan's Shuzo Matsuoka at Wimbledon in 1995.
Fifth-seeded Roddick sent down 38 aces in defeat.
Lu next will face Novak Djokovic.