"Tesla is finally being run like a normal business," the former GM vice chairman said on "Squawk on the Street."
"[Musk] finally reined in his costs," Lutz said. "He's reduced personnel and reduced unnecessary expenditures and has basically done what any other businessman would do in a situation where you're selling a bunch of stuff but you're not profitable" on a sustained basis.
In October, Tesla reported a surprise third-quarter profit as part of a strong stretch of months for the carmaker. Along with the completion of its Shanghai factory and better-than-expected fourth-quarter deliveries, shares of Tesla more than doubled since late September, trading as high as $498 in Wednesday's session.
Lutz, who retired in 2010 after 47 years in the auto industry, had previously said he thought Tesla was "headed for the graveyard."
"They will never make money on the Model 3 because the cost is way too high," Lutz said in September 2018. "He's got 9,000 people in that assembly plant producing less than 150,000 cars a year. The whole thing just doesn't compute."
But the situation, particularly regarding the Model 3, has dramatically changed, Lutz said Wednesday. Tesla has "achieved a volume break through, with the plant in China opening and selling a lot of Model 3s," he added.
Lutz said that accelerating Model 3 sales, especially ones with bells and whistles, have been aided by its perception as a high-end alternative to cars from BMW or Mercedes-Benz. He said he believed, when factoring in additional features, a lot of Model 3s were actually selling around $55,000 to $60,000.
"As long as they can keep that premium pricing, which is as I say about $33,000 over where they had originally talked about, obviously that car is going to be profitable," Lutz said.
Tesla had previously advertised plans for a $35,000 version of the Model 3, but the approach was significantly altered in the spring. In October, Tesla raised the price of its most affordable version of the Model 3 about $500 to $39,490.
Even so, Tesla's Model 3 has actually contributed to an overall decline in the average price of electric vehicles, according to data from Cox Automotive that publication Inside EVs reported on. The average cost to buy an EV in the U.S. in September was around $56,000. One year earlier it was around $64,000, according to the Inside EVs report.
Lutz said he also thought Musk, who is known for his sometimes eccentric personality and bold predictions, has moderated.
"He has been quite adept," Lutz said. "The encouraging thing to me about Tesla is from Elon there is less talk, less bluster ... he is focusing on the business, focusing on the product and focusing on cost control."