Tesla's board should thank Elon Musk for a "job well done," and then politely ask him to step down as CEO, Bob Lutz, former vice chairman of General Motors, told CNBC on Friday.

"The company is one disastrous mess," Lutz said in a "Squawk Box" interview. "There's no question Elon is a genius creator, a dreamer. The world needs people like that. The trouble is they usually can't run things very well."

Tesla did not immediately respond to CNBC's request for comment.

Tesla's stock was 12 percent lower in Friday's premarket, a day after Musk was sued by the Securities and Exchange Commission for alleged fraud. Musk was accused of making false and misleading statements in an Aug. 7 tweet about potentially taking Tesla private. The take-private idea has since been abandoned.

Tesla and the SEC were close to a no-guilt settlement, but Musk reportedly pulled out of the agreement at the last minute.

Thursday evening, Tesla and the company's board issued a statement backing the CEO, saying Musk has "integrity," and his leadership "has resulted in the most successful U.S. auto company in over a century."

Lutz, a longtime critic of Tesla and Musk, has claimed the electric car maker is "hemorrhaging cash" and because of the federal investigation, the SEC will not let it make a capital raise.

"They will never make money on the Model 3 because the cost is way too high," Lutz said earlier this month. It's an automobile company that is headed for the graveyard."

Musk had been acting erratically for months even before the take-private tweet.

In May, Musk rudely cut off analysts on Tesla's first-quarter earnings call. He apologized during the second-quarter call in August.

Musk was also launching tweetstorm after tweetstorm all summer as he was dealing with production problems for the company's new, less-expensive sedan, the Model 3.