During the first week of September as the Lance affair became a crisis, President Carter's top economic policymakers met over breakfast and reached an informal agreement that is building consternation through Wall Street.

The agreement: When Arthur Burns concludes eight years as heads of the Federal Reserve Board next January, he should not be reappointed chairman - not even for a two-year short term. That means Carter must overrule his senior advisers to keep Burns running the nation's central bank.

To Washington insiders who all year have regarded Burns as done for, this may seem like a dog-bites-man story. But to the shaky world of high finance - not only Wall Street but also Tokyo, Frankfurt and Zurich - it is a shock. Fairly or not, the money men regard sacking Burns as a Carter decision not to fight inflation. The consequences of that preception can only further stall sluggish capital investment.

The politically important timing of the breakfast meeting shows how shaky Burn's future is. With Lance's prospects for survival at that time virtually hopeless, there was speculation at middle administration levels that Burns might be needed at the Fed to reassure business after the departure of the budget director.

In fact, there was no sign this was even discused over bacon and eggs in the White House. Present were Treasury Secretary W. Michael Blumenthal, Chairman Charles Schultze of the President's Council of Economic Advisers, and Stuart Eizenstat, chief domestic policy adviser. Burns's future was not a formal agenda item, but his name came up in conversation. All three agree a new face was needed at the Fed in January.

Only Blumenthal's position was slightly surprising. He has developed an amiable relationship with Burns over weekly breakfast meetings and refrained from criticizing the chairman, publicly or privately, when action by the Fed boosted interest rates last spring. But like Eizenstat and Schultze, he believes Burns should go.

Lance, preoccupied at the time with his own survival, was not present at the September breakfast and will not discuss the Burns question. But he has been publicly critical of Burns's money-management policy, and friends say Lance months ago recommended against reappointment.

With the administration's economic high command in agreement, there would be no doubt of the final decision if Gerald Ford were President Jimmy Carter is not that predictable but it is difficult to see how he would reappoint Burns, unless strong countervailing advice came from somewhere. So friends of Burns would like to see pro-Burns whispers put in the President's ear by tow canny, business-oriented Washington power brokers: Sen. Russell B. Long (D-La.) and Robert Strauss.

Long's course is beyond either manipulation or prediction. As for Strauss, the incapacitation of Lance has broadened Strauss's duties as trade negotiator to fill in as informal emissary to the business world. But there is no sign he feels any differently about Burns from Carter's other senior advisers.

That leaves Burns himself to try to move the President. But while he would like to finish his career with two more years at the Fed, he has informed friends that, at age 73, he is not about to plead on bended knee to keep his office.

Consequently, since that breakfast meeting, word of the prospective sacking of Burns has spread through business circles, with nearly universally unfavorable connotations. "The pygmies have taken over and are getting rid of the last giant," one Washington-based business consultant informed us. What's more, he is sending that same message to his client corporations worldwide.

In search of mitigation, business executives are seeking names of possible successors who are on the conservative side and who favor on independent Fed. Those hopes were nearly extinguished by the name that most consistently crops up in Washington: liberal economist Arthur Okun of the Brookings Institution. Others mentioned - Schultze, econometric forecaster Otto Eckstein, businessman Andrew Brimmer (a former board member at the Fed) - are only sightly less disconcerting.

Pros and cons of Arthur Burns's record at the Fed cut across party and ideological lines. But nobody disputes his singular image as a conservative totem whose burning would point to diminished interest in combating inflation, in the eyes of business. Whether those consequences will be adequately presented to the President before he makes his decision is today in question.