Due to mistaken information from the publisher Little, Brown, it was incorrectly reported in yesterday's Style section that Harper's magazine editor Lewis Lapham had an indefinite amount of time to complete his work in progress, "Wealth in America." In fact, the contract deadline is March 1, 1982.

Lewis Lapham's resignation last week as editor of Harper's magazine is still the subject of confusion and controversy in publishing circles.

Lapham, 46, a 10-year veteran of the magazine and editor since 1975, announced his resignation on Aug. 14. "I want to devote more time to writing," Lapham said at the time. "I'm late with a book contract and I write a newspaper column, so now it's time to get out in the world more."

Harper's publisher David D. Michaels said yesterday that a new editor will be chosen soon from among a dozen candidates, "some of them very big names," and approved by the magazine's board shortly after Labor Day.

He characterized Lapham's departure as "entirely voluntary . . . there were lots of personal reasons for needing the time now." But he conceded that the Harper's board has been dissatisfied for some time with the design of the product, among other concerns. "Lewis likes it as it is, I don't," said Michaels, who was named publisher three months ago. He is about to choose a new designer and says future issues will appear "livelier." The editorial content will probably be "a little more upbeat. It's not known for its levity at this point."

Many in the New York publishing world believe that Lapham's resignation was a foregone conclusion since last summer, when the 131-year-old monthly, faced with declining national advertising revenues, was threatened with financial collapse. The John D. and Catherine T. MacArthur Foundation of Chicago stepped in with an infusion of funds to save the ailing publication, then owned by the Cowles publishing group. At that time, Lapham said last week, officials of the foundation asked him to stay on as editor and he agreed. But when the resignation was announced, "I don't think anybody was surprised," says a New York literary agent, who had expected the departure for four months, ever since "all of a sudden he started paying twice what he had been paying for articles."

"There are two inaccurate theories" about the resignation circulating in New York, Michaels said. "The first -- if you can believe it! -- is that Lewis is leaving because he's sore at the board for not giving his secretary a raise." That has been entirely disproven, Michaels said, and a magazine printing the story is issuing a retraction. "The second is that the board is dissatisfied with Lewis." Lapham denied this last week. And the MacArthur Foundation was not involved in the issue at all, according to Norton Kay, director of public relations for the foundation. Kay said yesterday that although the organization technically has owned the magazine since last August, "we've had a hands-off policy since then," and has no voice in editorial decisions.

There also has been considerable speculation in New York literary circles that Lapham resigned at least partly as the result of widespread outrage at a two-part article entitled "Panic Among the Philistines," which appeared in the August and September issues. The hostile polemic about loss of standards in the American publishing industry prompted a number of authors to complain to Lapham. Kurt Vonnegut, who calls the article "tinhorn Menckenism," said yesterday that he told Lapham it was "slovenly." Michaels denies that the controversial series influenced Lapham's resignation: "The magazine is run by a board that does not believe in censorship."

In the past, Harper's has often appeared nearly identical to The Atlantic, and until this month they shared a common marketing and advertising company: Harper-Atlantic Sales, Inc., which both publications have agreed to disband as of Sept. 1. Over the next year, Michaels said, "the identities will unmerge," as Harper's gets a new look and its own sales staff.

Lapham, who could not be reached for comment yesterday, is living in Newport, R.I., and working on a sociological study entitled "Wealth in America." Lapham is under contract to Little, Brown; but, "It's not like he had to have this book done by the end of the year or be defenestrated," Richard McDonough, Lapham's editor, said yesterday. The book is tentatively scheduled for publication in 1983.