Across Lafayette Park from the White House sits the massive limestone-faced headquarters of the U.S. Chamber of Commerce, a normally staid bastion of free enterprise which recently has been shaken by a feud between its two top officials.

On one side is Richard L. Lesher, the chamber's 49-year-old president, who has given the business and industry trade association a more activist stance in his seven years at its helm.

But the direction he took the chamber during the election campaign -- and earlier during the debate over last summer's tax increase -- brought him into conflict with the chamber's current board chairman, Paul Thayer, who is chairman of LTV Corp. of Dallas. The dispute between the two during the past several months came to a head last week at the quarterly meeting of the chamber's board of directors.

Under Lesher the chamber has been transformed from a typical trade association that simply seeks to represent the diverse views of its members. Lesher, with the approval of the chamber's board, has taken the organization on an ideological path fashioned by him and his closest aides.

His chief cause has been supply-side economics, which calls for tax cuts to spur savings, investments and growth. "The first economic policy of this great nation was a supply-side tax cut against King George," Lesher said in an interview.

Lesher also has presided over a major expansion program, which while more than doubling the chamber's membership to 250,000, has put a strain on the association's coffers.

Thayer, whose will and ambition is at least equal to Lesher's, maintains a powerful corporate presence in Washington. He is considered a political sophisticate who enjoys easy access to the Reagan White House.

The two first clashed last summer when Lesher, who had been one of the staunchest supporters of Reagan policies, suddenly broke with the administration in leading the chamber against the proposed tax increase. He even refused to let the White House use the chamber's new television studio to make a film promoting the measure.

But Thayer had endorsed the tax proposal during visits to the Oval Office, and was disturbed that the chamber, of which he is chairman for a year, was opposing Reagan, and became angered when he learned that access to the TV studio was denied.

Arguing that his stand was consistent with the board's wishes, Lesher said that "our board visited the tax issue over and over and over" and that Thayer was "looking for a way to support the president."

In August, Thayer called a special meeting of the chamber board to press for a reversal of the stand. He was unsuccessful, however -- a reflection of the powerful friends Lesher has on the board.

Thayer backed off and let the feud simmer, then last week sounded the bell for round two of his bout with Lesher.

The scene was the quarterly meeting here of the board of directors. On Tuesday night the chamber held a dinner at the Corcoran Gallery for about 50 corporate executives who sit on the chamber board, with Thayer presiding over the outwardly harmonious occasion.

Early the next morning, the chamber's staff was set to give the usual briefing to the members before the board went into executive session in the afternoon. But when Thayer arrived, he dismissed the staff members and immediately called the board into executive session.

According to board members present, Thayer launched into a monologue on how the staff of the chamber, particularly Lesher, should be more responsive to the board.

Thayer and others were particularly upset by the partisanship of the chamber's "opportunity list" of candidates during the recent election campaign. The list of about 100 favored candidates for the House and Senate did not include the name of a single Democrat. At the same time, a "hit list" of those opposing the favored candidates were all Democrats. This brought outcries from many of the targeted Democrats, as well as from local chambers which were backing Democrats.

When Thayer finished, Lesher spoke. The president, who enjoys the backing of such powerful board members as Pepsico chairman Donald M. Kendall and Jay VanAndel, chairman of Amway, defended his attempts to shake the chamber out of lethargy. Some directors present said later they were impressed by Lesher's performance.

But this time Thayer seemed to prevail, and the board adopted a resolution whose wording appears to tighten the leash on Lesher. The document, which was not made public, says in part that "the board should be given the opportunity to consider significant acts or matters of potential controversy involving the implementation or interpretation of policy."

It concludes, "The president shall keep the chairman informed of proposed actions that may be fairly regarded as significant or controversial."

In an interview the day after the board meeting, Lesher said he viewed the resolution as "a reaffirmation of existing by-laws. In our institution, the board of directors is in charge."

But Lesher did acknowledge that at least one of his controversial policies -- the "opportunity list" -- will be changed. "We will continue to be extremely active in political action. On the other hand, we will review that whole procedure," he said.

Lesher, who reportedly earns an annual salary of $212,000, runs the chamber from a paneled office richly decorated in the manner of a men's club, with pictures of bird dogs and sylvan themes.

His dispute with Thayer is not the first time that Lesher has brushed with controversy. Soon after joining the chamber in 1975, Lesher acquired a reputation as a tough talker by labeling Esther Peterson, President Carter's consumer adviser, "a woman scorned" after she criticized him for opposing establishment of a consumer agency.

More recently, he was quoted by a West Coast newspaper columnist as advising the unemployed to "get off their asses." Citing the quote, an AFL-CIO newspaper noted that the chamber itself had added to the unemployed roles by laying off some 30 employes.

The chamber's own financial problems are caused by a deep deficit. Its most recent financial disclosure shows it has depleted its capital and is running a $10 million deficit. Because of a change in its accounting year, the next audited statement will be made public in April, 1983, nearly two years after the last report, which was for fiscal 1981.

However, the business executives who sit on the chamber board show little concern about the deficit. At last week's meeting, the board members committed themselves to raise $35 million in new capital for the chamber, $18 million of which is to replace money already spent.

The major cause of the chamber's deficit is its $4 million television studio. In the few months of operations, only a handful of companies have subscribed to BizNet, a five-hour daily program of business and political news. But Lesher, who seems to enjoy his new celebrity from appearing on programs produced at the station, is not discouraged.

During the past month he dispatched two of his aides to explain to board members, in anticipation of last week's meeting, that the current financial bind caused by the television facility was temporary. And at the board meeting he spoke glowingly of the future of BizNet.

He proudly notes that the studio has been a lure to powerful politicians. "Prior to this fall we had one sitting president ever in this building," he said. "In the space of four weeks, we will have had the president here three times [to use the studio]. And half the Cabinet, too."