On a day of injuries and shocks - the victims including Murray's potential quarter-final opponent Jo-Wilfried Tsonga - the world number two left Court One with his title prospects enhanced.
As in his first-round win over Benjamin Becker, Murray looked in fine fettle and ran out a 6-3 6-3 7-5 winner in a minute over two hours and next meets Spanish 32nd seed Tommy Robredo.
The British number one has played one match on the second court in each of the last three years and began confidently on this occasion.
But Lu, who beat Andy Roddick here to reach the quarter-finals three years ago, was pushing the pace, particularly on his forehand, and in the fifth game he forced three break points.
He did not make one return though, his first effort an especially ill-advised forehand that did not threaten the court.
Not taking his chance seemed to deflate the Chinese Taipei player, who was immediately broken, and, although he saved two set points in the eighth game, Murray wrapped it up with an ace.
The pair had played twice before, winning once each, with their first match coming in the opening round of the Beijing Olympics in 2008.
It was a particularly painful loss for Murray, who got too caught up in the Games experience and did not prepare properly.
The defeat made him doubly determined to contribute to the British medal haul last year in London, where he came away with gold and silver.
He had no problem with his footing or anything else and began the second set with another break of serve.
The second seed was threatening in every Lu service game and in the ninth game another terrific forehand earned him a first set point.
Lu saved it with a fine backhand, and then a second that followed, but on Murray's third chance his opponent double-faulted to hand the Scot the set.
Murray's last defeat on grass came in the Wimbledon final last year against Roger Federer, with the Scot winning 12 matches on the surface since before this contest, a record he improved.
Lu had beaten James Ward in the first round to scupper thoughts of a rare all-British clash, but he had nothing with which to hurt Murray.
The second seed forced a break point in the sixth game of the third set, and showed just how much he wanted every point by whacking his foot in frustration when Lu's shot trickled off the top of the net.
The world number 75 eventually came through a very long game, and he was showing a good deal of courage in hanging on.
Murray's first match point arrived with Lu serving at 5-4 behind, but the underdog came up with a big serve when he needed it most.
He could not do the same in his next service game though, Murray clinching victory on his third match point when Lu sent a backhand long.