The 10th-seeded Roddick won the first set easily, but Lu picked up his game in the second, rushing the net repeatedly and hitting 15 winners to eight for the American.
The former U.S. Open champion then broke Lu twice in the third set to close out the match.
Roddick was beaten by Lu in five sets in the fourth round of Wimbledon last year, the last time the two players met. But the Taiwanese player made too many mistakes Monday, committing 50 unforced errors, including seven double-faults.
"He plays so high risk," Roddick said. "Overall, I thought it was pretty good, save four games."
The 29-year-old Roddick has struggled to regain his form this season, losing in the third round at Wimbledon and pulling out of the French Open because of injury. His ranking has slipped to No. 15.
Last week, he lost in the first round of the China Open in Beijing, falling in straight sets to Kevin Anderson of South Africa in a loss he later called "unacceptable."
"It's been tough. It's been, I think, the toughest year I've had. I feel like I've been starting and stopping a lot," Roddick said. "You know, I'm going to probably have to adjust how I go about things a little bit more. Running myself into a wall with work and everything else, I don't know that I can do that without getting hurt. It's happened numerous times this year. I might have to work smarter from now on."
Also, Bernard Tomic of Australia overcame 25 aces from Anderson to beat the South African 7-6 (5), 6-7 (4), 6-3. Tomic won despite converting only one of 12 break points in the match.
"He's so tough because his serve, he gets his corners and gets you out of the court," said Tomic, who reached a career-high ranking of 49 this week. "Playing a lot of these guys, they serve one style. He serves every serve and serves well. You can't really get on his serve."
David Nalbandian of Argentina beat Ernests Gulbis of Latvia 7-5, 6-4, Grigor Dimitrov of Bulgaria defeated Marsel Ilhan of Turkey 2-6, 6-1, 6-4, and Albert Montanes of Spain beat Mikhail Kukushkin of Kazakhstan 6-2, 5-7, 7-6 (5).
The Shanghai tournament, the only Masters event on the ATP tour's autumn Asian swing, has been hit by a number of withdrawals this year. Top-ranked Novak Djokovic pulled out to recover from a back injury and No. 3 Roger Federer is taking a six-week break to rest "nagging injuries."