Harper's, the perennially embattled journal of culture and opinion, yesterday got a new editor and a new identity.

The board of Harper's Magazine Foundation voted to bring back columnist and author Lewis Lapham, 48, who had edited the volatile monthly from 1975 until his abrupt departure in 1981. And it endorsed his plan for a complete restructuring of the magazine along topical lines, scheduled to begin by the end of the year.

Board president Rick MacArthur, 27--whose father heads the MacArthur Foundation, which swept in to rescue the financially ailing magazine in 1980--said yesterday from Harper's New York offices that during the past two months about 15 other candidates were considered, "some of the top people in the magazine business," but none "could come up with an idea that would differentiate us from the Atlantic." But with Lapham's concept, he said, "we can capture a larger audience. It will make us unlike any other magazine."

"Essentially," Lapham said yesterday, "it's going to be a new deal," consisting of three elements. "The first is a national op-ed page, a genuine forum" of six or seven signed opinions on a single issue. "If there is such a thing as a national debate now in this country, it takes place on the op-ed pages of about four newspapers.

"The second is the annotation of texts--testimony, transcripts, speeches and documents" about major topics of the day. Each will be annotated with "explanations and explications" by an expert on the document's subject. Most are likely to be political or economic, but "we could also take a transcript from 'Dynasty' and annotate it," or juxtapose a piece of literary commentary with the B. Dalton best-seller list.

The third section, Lapham said, will be "a summary and synopsis of the month's events" in science, culture, economics and politics: "partly original writing, partly reprinted from foreign papers, scientific journals and obscure literary quarterlies," and with "commentary throughout knitting it all together."

There may be "the occasional major essay, but only when you've got it," he said. "Most of the stuff will be relatively short and topical," intended to "illuminate and make connections" among contemporary trends. "It will be a much less opinionated magazine. And I'm not going to write for it," continuing instead with his syndicated newspaper column. The fate of the present staff is uncertain, Lapham said, since "I don't even know who these people are, really." Helen Rogan, the highly regarded acting editor, will temporarily oversee articles already commissioned.

Six of the board's nine members convened yesterday; of those attending, a majority voted for Lapham, said chairman Leon Botstein. Among Lapham's strongest backers, he said, were Walter Cronkite and George Ball. Other members include Daniel Yankelovich, Elizabeth McCormack, Lisle Carter, Nikolai Stevenson and Richard LaPere.

During the past 18 months Lapham had submitted roughly similar proposals elsewhere--one to learned institutions, another to National Endowment for the Humanities. When word of his possible return to Harper's began circulating two weeks ago, reporters started receiving anonymous letters from New York disparaging his personality, implying that he would ruin morale at Harper's, and alleging that he had been dismissed in 1981 for chronic overspending.

"They're welcome to their opinion," Lapham said, "but I never exceeded the budget at all," and left "in part because I couldn't work out an agreement with the board about what direction the magazine was going to go in."

The identity problem had long nagged the board, MacArthur said, since "the general public perception is that the Atlantic and Harper's are the same magazine practically." That condition, he said, had not improved under former editor Michael Kinsley, whose frequent altercations with the board culminated when he left Harper's last month for The New Republic, where he will begin writing the TRB From Washington column in the fall. But now "I'm excited," said MacArthur, a former newspaper reporter and free-lance writer. "I'm going to promote this thing full-time. I feel a personal responsibility to make Harper's permanently self-sustaining--no charity case." Most of the magazine's bail-out funding--$1 1/2 million from the MacArthur Foundation and a matching sum from ARCO--is still intact, he said. And with a circulation of 140,000, "we only lost $300,000 last year." Botstein said he was optimistic that growing national concern over standards of literacy and an aging population would mean that "this kind of magazine may be coming back en vogue." And Lapham's plan "gives us the longest run with the most momentum."

Only a month ago, Harper's won the coveted 1983 National Magazine Award for "general excellence," which cited its "serious intellectual content" and "skepticism, verve and humor" under Kinsley's direction. "But Lapham has won a lot of awards, too," MacArthur said. "Kinsley tried to make it into much more of a biting, satirical, nasty journal. But the board in general wants a much more serious purpose. After all, we're a not-for-profit organization." Besides, "the magazine I convinced the MacArthur Foundation to rescue in 1980 was Lewis Lapham's magazine."