President Carter met secretly with Senate Majority Leader Robert C. Byrd (D-W. Va.) Monday night, and Byrd reiterated his previously stated opinion that Bert Lance should resign, well-informed sources said.

Last week senior White House aides said Byrd's reaction to Lance's self-defense before the Senate would be crucial to the political future of the director of the Office of Management and Budget.

One associate of the President's, encouraged by Lance's testimoney last Thursday and Friday, said: "If the sentiment of the Senate shifts there is a possibility that Sen. Byrd would take a different view."

The Senate Governmental Affairs Committee delivered another potential blow to Lance yesterday, releasing testimony from a federal official that contradicts Lance's own testimony last week.

The new testimony suggests Lance actively sought to clear up his record with federl bank examiners before his nomination to head the OMB was announced.

Carter has scheduled a news conference for 3 p.m. today, Jody Powell, his press secretary, discouraged speculation yesterday that the President might make an announcement on Lance's fate at the conference.

"So far far as I know," Powell said, "he (Carter) has neighter asked Lance to resign or to stay on."

Asked if the President was having trouble making up his mind, Powell replied: "There are no commitments on when the buck has to stop."

Byrd said to have told Carter that he still believes Lance's effectiveness has been destroyed. Moreover, Byrd is said to have warned the President about the sharp, partisan emotions that the Lance hearings provoked last week in the Senate committee.

The committtee yesterday released a new piece of testimony on the Lance affair that represents a direct challenge to the veracity of both Lance and Donald Tarleton, director of the Atlanta regional office of the comptroller of the currency.

The new testimony involves the events of last Nov. 22, when Tarleton decided to rescind a corrective cease-and-desist agreement between his office and the Calhoun, Ga., First National Bank, of which Lance was then chairman.

The cease-and-desist agreement was a potentially embarrassing document for Lance, because it described his and his relatives' overdrafts at the bank and criticized his management of the bank.

Tarleton and Lance both previously testified that Lance visited Tarleton on Nov. 22 to tell him he was going to be appointed director of the OMB.Tarleton has testified that Lance didn't mention the Calhoun bank agreement that day. Lance, disputing him, has testified that he did mention it, but only in passing.

Several hours after their meeting, Tarleton rescinded the agreement.

The new testimony released yesterday is from Michael M. Patriarca, an attorney in the enforcement division of the comptroller's office in Washington.

Patriarca has told investigators he had dinner with Tarleton last Fabruary, and in the course of a confidential conversation, Tarleton told him Lance came to his office on Nov. 22 and "said essentially the following:

"'Fimmy wants me to be the head of the OMB, and I want to go into it with a clear record, so I just wondered if you could see your way clear to lift the agreement on Calhoun.'"

Patriarca described this conversation to investigators from the Internal Revenue Service, who have conducting an inquiry into the comptroller's office's handling of Lance-related matters.

Patriarca volunteered his story last Saturday. He told the IRS he has not done so sooner "because of his pledge to Mr. Tarleton to maintain the confidential nature of their dinner conversation" last February.

His decision to divulge this information voluntarily to IRS investigators was prompted by the fact that testimony before the Senate Governmental Affairs Committee did not accord with the information Mr. Tarleton had previously told him," the IRS reported.

Patriarca told the IRS he had high regard for Tarleton as a bank examiner.

His testimony quoted Tarleton as saying that Lance offered to help out if he, Tarleton, "ever came across any situation in government that he didn't think was 'right.'" Tarleton took up this invitation, he told Patriarca, by writing to Lance after he took office in Washington to complain that the Justice Department was dragging its feet in an investigation against a bank officer in the Atlanta region.

According to Patriarca's story, this letter had some effect. Tarleton, Patriarca recounted, said he received a letter back from Michael Egan, the deputy attorney general, an Atlantan who is doing much of the day-to-day administration in the Justice Department.

Tarleton could not be reached for comment on Patriarca's testimony.

Rep. Fernand J. St Germain (D-R.I.) said yesterday he had asked the Justice Department to investigate whether Tarleton had committed perjury in light of the Patriarca testimony.

Tarleton's first sworn testimony that Lance had not asked him to rescind the cease-and-desist agreement was made before St Germain's House subcommittee on financial institutions on Sept. 6.

Lance played tennis with Carter yesterday at the White House. The two of them were a doubles team; they took on Carter's principal aide, Hamilton Jordan, and his speechwritter, James Fallows. No score was announced.