Murray, who saw off Benjamin Becker in straight sets in the first round, snatched a break in the final game of the third set to complete a straightforward win over Lu on Court One.
The number two seed was rightly wary of Taipei opponent Lu, who is a previous All England Club quarter-finalist and famously beat the British number one in the first round of the 2008 Olympics.
But the world number 75 was simply no match for the home favourite, who claimed his 14th straight win on grass - after victories at last year's Olympics and this year's Queen's Club - 6-3 6-3 7-5.
Murray was not at his very best but he never looked like losing, winning his first service game to love to underline an efficient and imposing performance on number one court.
"I kept my concentration and served very well throughout the match and gave him very few opportunities," said Murray.
"He made it a bit tougher in the third set, so I did well get through in three sets. You can't guarantee any match is going to be easy and you need to do whatever you can to progress as easily as possible."
He has always said one of his biggest tennis regrets was his lacklustre display in Beijing - a wrong he righted with Olympic gold last summer.
But this was revenge served cold for Lu, whose unforced error count was a little too close to his miserable second serve statistics.
Despite an improvement from Lu in the third set, Murray polished off points with a flourish, whipping forehands across the court and down the line as his rival hurried, scurried and wafted his racquet at thin air.
He will now take on Spain's Tommy Robredo, who beat France's Nicolas Mahut, but his most likely quarter-final opponent, France's Jo-Wilfried Tsonga, was forced to pull out of Wimbledon through injury.
Round 2 results:
2-Andy Murray (Britain) beat Lu Yen-Hsun (Taiwan) 6-3 6-3 7-5
Sergiy Stakhovsky (Ukraine) beat 3-Roger Federer (Switzerland) 6-7(5) 7-6(5) 7-5 7-6(5)
Ernests Gulbis (Latvia) beat 6-Jo-Wilfried Tsonga (France) 3-6 6-3 6-3 0-0 (Tsonga retired)
Kenny De Schepper (France) beat 10-Marin Cilic (Croatia)WO
15-Nicolas Almagro (Spain) beat Guillaume Rufin (France) 7-5 6-7(6) 6-3 6-4
Adrian Mannarino (France) beat 18-John Isner (U.S.) 1-1 (Isner retired)
20-Mikhail Youzhny (Russia) beat Vasek Pospisil (Canada) 6-2 6-7(3) 7-6(7) 3-6 6-4
22-Juan Monaco (Argentina) beat Rajeev Ram (U.S.) 5-7 6-2 6-4 6-2
24-Jerzy Janowicz (Poland) beat Radek Stepanek (Czech Republic) 6-2 5-3 (Stepanek retired)
25-Benoit Paire (France) beat Stephane Robert (France) 6-4 7-5 6-4
Fernando Verdasco (Spain) beat 31-Julien Benneteau (France) 7-6(1) 7-6(4) 6-4
32-Tommy Robredo (Spain) beat Nicolas Mahut (France) 7-6(3) 6-1 7-6(5)
Viktor Troicki (Serbia) beat Andrey Kuznetsov (Russia) 6-4 6-3 6-4
Dustin Brown (Germany) beat Lleyton Hewitt (Australia) 6-4 6-4 6-7(3) 6-2
Lukasz Kubot (Poland) beat Steve Darcis (Belgium)WO
Jurgen Melzer (Austria) beat Julian Reister (Germany) 3-6 7-6(2) 7-6(5) 6-2
- Sports & Recreation