Lagging hopes of business that President Carter might yet avert another wound to the economy were heightened a little Nov. 14 when Rosalynn Carter lunched privately with Arthur Burns, chairman of the Federal Reserve Board.

Although her viewpoint is wrapped in mystery, nobody denies the First Lady's status as a serious adviser to the President. Thus, advocates of Burns took hope that the Monday luncheon covered more than its announced subject of "voluntarism." If she reported favorably to the President on Burns, it would break the present pattern that points to more Carter trouble with the economy.

That pattern: blanket opposition to reappointment of Burns as chairman of the Fed from the President's own advisers (except for Treasury Secretary W. Michael Blumenthal, who is ambiguous); blanket insistence from outsides in the business world that forcing Burns out Jan. 31 is one piece of bad news not yet discounted by money markets.

Such news will be interpreted as proof that the administration is eyeing the inflationary course and does not want Arthur Burns around to blow his whistle. Reverberations at home and abroad are why even frequent critics of Burns - economists Eliot Janeway and Pierre Rinfret, and economic pollster Albert Sindlinger - publicly urged that he be retained.

This position had surprising support among congressional Democrats - such as Rep. Thomas Ludlow Ashley of Ohio, a rising figure in the House thanks to his gritty performance as chairman of the ad hoc energy committee. Ashley, highly regarded in the White House, this week privately urged the President to reappoint Burns.

A flickering possibility that Ashley's advice might be taken exists because the President has neither made up his mind nor discussed the subject in formal meetings. Still, unless Mrs. Carter was so charmed over lunch that she becomes a Burns booster, the President is far more likely to hear a negative message on Burns wherever he turns.

There has never been doubt that chief domestic aide Stewart Eizenstat and chief economic adviser Charles Schultze want Burns out. Less well known is how deeply anti-Burns feeling is rooted in the President's inner circle. Contending that the 73-year-old central banker now is the product of old press clippings, one senior adviser told us: "Burns can't fill his own shoes." A key political aide with no pretensions to economic expertise tells the President that Burns must be replaced or Jimmy Carter will face the wrath of organized labor and Democratic politicians.

The influential Jody Powell fits this category. After the President praised Burns at his last press conference, press secretary Powell toned it down at the next day's press briefing. When the President lunched with Burns and Treasury Secretary Blumenthal that day, Carter informed the Fed chairman: Jody said I was too nice to you.

But being "too nice," say white House insiders, is just part of a White House tactic of pacifying business and the money markets with pro-Burns rhetoric until the time comes to dump him - a tactic with unfortunate time limitations. Whether Blumenthal's panegyric on Burns before the Senate Banking Committee is part of the same tactic is less certain.

During a recent trip abroad, Blumenthal became less cavalier about the declining state of the dollar and might be connecting the dollar's health and Burn's future. Overriding Schultze's objections, Blumenthal insisted that Burns review the Humphrey-Hawkins jobs proposal.

But Blumenthal, still blamed at the White House for pushing Bert Lance, might not want to swim upstream on this issue. Behind his public praise, Blumenthal over dinner the other night expounded privately on how many sound conservatives could replace Burns (a discussion described as "disquieting" by a Burns man present).

Those remaks by Blumenthal exposed the administration's desire to name somebody who would cushion Burns's departure. But two names prominently mentioned, ex-Treasury Secretary Henry H. (Joe) Fowler, 69, and Republican Bruce MacLaury, 45, head of the Brookings Institution (and former president of the Federal Reserve Bank of Minneapolis), provide little cushion. MacLuary means nothing to business and Fowler is viewed as somebody who might take orders from Schultze.

Republican consultant-lobbyist Charls Walker will urge Burns, If he is dumped as chairman, to stick around as a board member. He might do it if he considers his successor a weakling. Since the head of the table then would be where Burns sits, the administration would have managed the worst of all worlds: economic trauma resulting from sacking the old man without actually getting rid of him.