If it's a challenge that Drew Lewis wanted when he left his post as secretary of transportation six months ago to return to the private sector, it's challenge he's found at Warner Amex, the nation's fifth largest cable operator.

While known for his ability to deal with problems, Lewis, 51, admits to knowing little of the cable business, little about entertainment, and, in fact, seems to have little interest in watching television. A cable subscriber only since moving to Manhattan several months ago, he is just starting to learn what cable is all about.

Still, Lewis has not hesitated to make his mark on both the company and the industry.

The cable television business is beset by financial, marketing and regulatory problems, while Warner Amex, which has 1.34 million subscribers, is confronted with the complex and costly task of wiring a host of cities. And the two companies that own Warner Amex--Warner Communications Inc. and American Express Co.--are uneasy partners.

"It's the parents that are troubled, not the cable company," says a source close to the venture. On Warner's side are the continuing federal investigation of the company's Westchester Premier Theater transactions (which involve allegations of kickbacks to Warner executives to buy stock in the theater), the bottom-line difficulties of its Atari subsidiary, and a related insider stock trading investigation.

On the American Express end are the strained efforts to join the credit card and travel giant's operations and leadership under Chairman James D. Robinson III with those of the Shearson brokerage house and its top official, Sanford I. Weill, now president of Shearson/American Express.

A further complication is American Express' uneasiness with its cable venture and its losses. Sources close to the company contend that American Express would love to sell off its interest in Warner Amex and periodically tries to do so.

"Our view at this point is that the business is bottoming out and will turn up," said Louis V. Gerstner Jr., chairman and chief executive of American Express Travel Related Services Co. Inc. and its top liaison with Warner Amex. "We've lived through the toughest part and the rest of our businesses are doing so well that the obvious strategy for us is to see this thing through."

Another weight on Lewis is the continuing pressure from top Reagan administration officials and other leading Republican politicos to play an active, leadership role in that party's affairs, particularly if Reagan runs for reelection. For now, however, Lewis' only commitments are to the firm and to be a "volunteer" in a Reagan reelection effort.

But Lewis, after playing a key role in securing Senate passage of cable television deregulation legislation, has decided to take on the additional responsibility of lobbying members of the House on the controversial and politically sensitive bill. The legislation is vigorously opposed by American Telephone & Telegraph Co. and many officials of city governments.

The biggest surprise Lewis has run into in his job, he says, are "the internal conflicts within this organization." He has, therefore, moved to decentralize the firm's operations, particularly in the marketing area.

At the same time, he's eliminated 77 of 355 central staff jobs in the New York area, raising anxiety within both the headquarters and field operations.

Lewis also has ruffled the feathers of the cable establishment, primarily the National Cable Television Association and its top staff and executives, by his aggressiveness while pushing Congress toward deregulating the business.

"He's intimated that they cable lobbyists did not know what they were doing on the Hill," said a source close to the cable hierarchy. "They came in shooting up the saloon. They came in hard and late," another industry source says of the role of Warner Amex and Lewis in the legislative fight.

On the other hand, key Senate supporters of the cable legislation, like Sen. Bob Packwood (R-Ore.), say Lewis' efforts were invaluable, particularly in heading off an amendment introduced by Sen. James Abnor (R-S.D.) that would have required state regulation of new cable services.

Lewis also angered several key officials in the cable industry by a blunt statement quoted in the Dallas Morning News at the time the Senate cable bill passed. Lewis said that if the measure became law, loosening city government authority over local cable systems, Warner Amex would feel free to abandon unprofitable cable systems.

"In the broadest sense we're really not a free-enterprise business," Lewis said the other day. "We're sort of a quasi-pubilc utility that doesn't get a return on its rate base but yet has its prices controlled.

"I'd prefer not to, but if you want to, make us a public utllity and give us a return on our rate base. I'll settle for that right now. If not, let us compete in the free marketplace with the Pittsburgh Pirates where the company has a cable franchise , the symphony and the local movies.

" . . . These cities don't have a great deal to regulate, so it's fun to regulate cable television. You can put all your time and effort in for a 15-year contract and then the mayor's brother-in-law decides he wants to be in the cable business and he gets the franchise.

"If we get caught in that kind of political crossfire . . . they city governments are going to end up with the systems back in their laps and its going to be public transit No. 2," Lewis said, referring to the transportation problems he dealt with at DOT. "We are positively not going to stay in any city where we can't make money. No one else is either."

His tough bottom-line orientation is what primarily made Lewis appealing to the two parent companies and it's what Wall Street analysts like about him. "He's extremely impressive--well spoken and rational," said analyst John Reidy of Drexel Burnham Lambert Inc. "If anybody can pull that business together, its a guy like Lewis. He strikes you as very professional, and realistic, too."

Along with his cable deregulation and internal streamlining efforts, Lewis also has made changes in Warner Amex's programming business--the popular but unprofitable MTV, the 24-hour-a-day rock video service, Nickelodeon, a children's programming service, and The Movie Channel, the third largest pay cable venture. The Movie Channel is trying to find a way to restructure itself after the Justice Department raised antitrust concerns about a proposed merger with Showtime, the second largest pay service.

Lewis is trying to make MTV's revolutionary approach to rock music profitable by charging cable systems that carry it--it brings in advertising revenues as well--and has added advertising, for the first time, on Nickelodeon, a move that angered children television activists but sits well with analysts and most others in the industry.

What draws attention to Lewis' views and actions is the fact that he is the highest ranking executive from outside the industry in many years. And he says that works in his favor.

"I've said I don't know anything about show business," he said. "But if you don't know what things you can't do, you can do them," he said.

He does know something about turning around difficult operations and that's what he faces at Warner Amex. In 1982, the cable venture had revenues of $307.6 million and operating expenses of $402.8 million, leading to an after-tax loss of $46.6 million. That occurred even though 136 of 143 of the firm's cable systems showed a profit last year.

But its the other seven systems, those in Pittsburgh, Columbus, Houston, Dallas, St. Louis, Cincinnatti and Chicago, as well as one under construction in Milwaukee and the programming ventures, that create the losses. And, by fall, the company is expected to sign in final form a franchise agreement to construct systems in parts of Brooklyn and Queens, a massive effort that will cost at least $300 million.

This year's losses will exceed last year's, even though Lewis expects the company's revenues to rise to about $500 million to close to $1 billion in 1985. But Lewis says the continuing losses represent the price to be paid for an investment in cable television. Company officials think they can begin to turn around those results next year, although profitability is still several years away, according to Lewis.

When asked by a top American Express official what the cable company's 1983 losses were likely to be, Lewis turned the question around and asked what that executive would like them to be.

"I didn't mean that in a manipulative sense," he recalled. "From a business standpoint, there's a tremendous capital investment here that is worth every bit of the investment that's been made. I told them that if they're unhappy with these losses, tell me now. I can lose less money than last year but if we do it's a mistake in terms of our long-term strategy."

"We're not a troubled company. Our loss after taxes is about a rounding off error for American Expresss," he noted. "We're a start-up company that's building our factory and you don't make any money until you get your factory built."

Will he be around to see profitability at Warner Amex? "I don't plan to be a short-termer," he said. "I would not leave here until I'm comfortable that this is a sound business. But the problems of this business will be solved before its profitable."