After a tough three-set victory over fellow American James Blake in the opening round, Roddick relied on his serve to turn back Taiwan's Lu, who saved seven break points but faltered in the second set at 4-4.
"As well as I did some things tonight, if I want to move through this tournament I've got to do better on break points," Roddick told reporters.
"I've very close to playing really well and it's just a matter of tighten up a couple things," he added.
Roddick, bidding for his third Memphis title, did not drop his serve as he clubbed 10 aces. He next faces fellow American Sam Querrey, who defeated Argentina's Leonardo Mayer 6-4, 6-0.
In the women's draw, top seed Maria Sharapova of Russia dispatched eighth seed Elena Baltacha of Britain 6-2, 7-5.
It was another commanding performance from Sharapova, who has yet to drop a set in Memphis, as she claimed a nip-and-tuck second set by breaking her opponent at 5-5.
Sharapova will play fifth seed Petra Kvitova of the Czech Republic for a place in the final.
Second seed American Melanie Oudin failed to join Sharapova in the last four, losing to unranked Swede Sofia Arvidsson 6-1, 6-3.
"She wasn't missing anything," Oudin said of her opponent. "She played a really good match and there wasn't much I could do," she added.
Arvidsson will play unranked Briton Anne Keothavong in the other semi-final.