Republican National Chairman Bill Brock yesterday declared that President Carter can retain Bert Lance as director of the Office of Management and Budget only if he is willing to break his promise to run a government "free of even the appearance of illegal or unethical conduct."

Stopping just short of an outright demand for Lance's resignation, Brock said that keeping Lance is "a frank admission that those high standards he [Carter] pledged in his campaign now have been violated."

Two influential House Democrats also challenged Carter's decision to retain the embattled budget director, but White House press secretary Jody Powell once again detended Lance and said he has done nothing to deserve being "run out of government."

Georgia Gov. George Busbee (D), who returned to Atlanta with Lance from the Southern Governors Conference in San Antonio, assured reporters that Lance "will be in Washington for a long time."

The two House Democrats who questioned the President's judgement on the issue were Budget Committee Chairman Robert N. Giaimo of Connecticut and Rep. Lee H. Hamilton of Indiana.

Giaimo called Lance "a political liability" to Carter, but said the President "can't develop the image of a man who will not fight for his friends." But ultimately, Giaimo said, "a president can't afford" to have an OMB director "who is crippled or hurt or ineffective."

Hamilton, a 12-year House veteran, said in a statement that "every new bit of information about Mr. Lance's financial actions only embarrasses the President and undermines the confidence of the people in Mr. Lance's ability to handle the federal budget.

"It is time, maybe past time, for Bert Lance to resign," Hamilton said.

At his regular White House briefing yesterday, Powell said the press is pelting Lance "with rocks and sticks" while the administration tries to defend him "with pillowcases."

Criticizing the fairness of the press coverage of the Lance case, Powell said, "I am frankly surprised at the amount of support for Bert Lance that exists in the public, considering the quality of information they've had to base their judgement on."

Powell singled out as "a real low point in the coverage" a story yesterday by the Chicago Sun-Times, printed in The Washington Post, which dealt with the relationship between Lance and John L. Moore, an official in the Carter transit on staff who has now been appointed by the President as head of the Export-Import Bank.

The story said that at the time Moore cleared Lance of any conflicts of interest last December he was the attorney for a bank to which Lance owed money and was a law partner of Lance's attorney.

The story quoted Moore as saying, "there is no question there is a conflict or an appearance of a conflict, but I didn't do anything that was not in the highest interest of the President-elect."

Powell said that while there might be "an appearance" or a "possibility" of a conflict, "there is no allegation based upon the fact that he conducted himself in any way improperly.

"To impugn a man's reputation based entirely on circumstance is a deplorable thing," Powell said.

However, in an interview Wednesday with the Los Angeles Times, Attorney General Griffin B. Bell expressed a different view. Bell said it would be "unusual" for Moore to review Lance's financial affairs for possible conflicts of interest while his law partner, Sidney Smith, was serving as Lance's attorney.

"It would be like [Charles] Kirbo clearing me, or me clearing Kirbo," Bell said. Bell and Kirbo were law partners in Atlanta before Bell joined the Carter administration.

However, Moore has said that he, Lance and Smith jointly drafted a statement explaining an earlier investigation by the comptroller of the currency into Lance's banking practices.