Federer, who is gunning for his fifth title at Melbourne Park, won 6-4, 6-2, 7-5 and will play Italian Simone Bolelli in the second round.
The 17-time Grand Slam champion reeled off the opening two sets in just over an hour but found more resistance from the 47th-ranked Lu in the third.
The breakthrough came in the 11th game when Federer held three break points on Lu's service and took the game when the Taiwanese overhit a forehand.
Federer served it out for the match, protecting his record of never losing a first-round match in 16 appearances in Melbourne.
"I thought it was played at a really good level, it was a tough match and I had to step it up," Federer said.
"I've played him a few times so I knew what he can do and he didn't disappoint," he said.
"It's early in the season and it's tough to get rhythm, especially in the first round, but this court plays nice and we had some great rallies so it was a nice match."
Federer has reached the semifinal stage at his last 11 Australian Opens.
He joined 14-time Grand Slam rival Rafael Nadal and two-time major winner Andy Murray in the second round.
Nadal, a beaten finalist to Stan Wawrinka last year, turfed out Russian Mikhail Youzhny in an uncomplicated straight sets victory, while Murray began a campaign hoping to end the heartbreak of three runners-up finishes in Melbourne.
The Scot emerged a 6-3, 6-4, 7-6 (7/3) winner over India's Yuki Bhambri.
Rising Bulgarian star Grigor Dimitrov, seeded tenth, also swept to victory over Germany's Dustin Brown in just 69 minutes, while Czech seventh seed Tomas Berdych blew away Alejandro Falla.
Australian teenager Thanasi Kokkinakis upset 11th seeded Latvian Ernests Gulbis in a dramatic late night five-setter, while Spain's 15th seed Tommy Robredo retired just five games into his match with Frenchman Edouard Roger-Vasselin.
Spanish world number three Nadal was delighted with his straightforward win over Youzhny, a former US Open semifinalist, and will next play American qualifier Tim Smyczek.
"Very positive result for me," he said.
"I think a very good start. Very important."
Nadal has had only seven matches since Wimbledon last July due to ongoing back and wrist injuries and an appendectomy.
His lack of match fitness was apparent in Qatar this month when he was humiliated in the first round by German Michael Berrer, a qualifier ranked outside the top 100.