Senior White House and Justice Department officials met at the White House yesterday to map a strategy aimed at using the final Senate debate on the Supreme Court nomination of Robert H. Bork to bolster chances that the next nominee will be approved.

Acknowledging that confirmation of Bork is all but impossible with 53 of 100 senators on record against him, administration officials are hoping the vote will be soon -- by Oct. 23 -- and that they will be able to refocus the Senate floor debate to emphasize the importance of judicial restraint.

The Saturday session came as President Reagan, repeating his defense of Bork, accused three Senate Democrats of leading a "lynch mob assault" on Bork and rejected charges that the administration had failed to make a strong enough case.

The day's planning at the White House and Reagan's continued attacks on Bork's critics reflected the almost surreal position in which the White House finds itself. Bork's refusal to follow the accepted Washington custom of withdrawing in the face of almost-certain defeat requires the administration to continue, at least nominally, the public battle on his behalf. But the reality of an administration nearing its end requires the White House to get on with finding a new nominee and securing confirmation as quickly as possible.

Although Bork's decision to stay in the fight increases the risk that the Supreme Court seat will remain vacant into the 1988 election year, administration strategists hope that Bork's emotional blast at what he termed the politicization of the confirmation process, and continued debate on that theme, will ease the way for a nomination if it stretches into 1988.

"The terms of debate for the next nominee will be set on this," a Justice Department official said. "I don't think that the opponents are now going to savage Bork," the official said. "I think what's at stake is an effort to rewrite what has happened, for {opponents} to try to show the public approves of activist judges, of judges who make up what the Constitution says as they go along."

The administration, the official said, will seek, in the debate over Bork, "to prevent the impression from being generated that that {activist judge} is the kind of judge the American people want."

"The strategy now is to maximize the vote, to frame the debate and set the record straight on Bork, and to set the stage so the next nominee doesn't have to go through the Bork agony," one administration strategist said.

"It's a fight for the judicial system," the strategist said. "Those senators {supporting Bork} do not want to allow this nomination to be the standard by which other nominees are to be judged in the future. Is this how we're going to name Supreme Court justices?"

Reagan is expected to speak out on Bork's behalf in various appearances this week, and administration lobbyists will contact the eight undecided senators, as well as those perceived as lukewarm in opposing Bork. For example, Sen. Howell Heflin (D-Ala.), at the Senate Judiciary Committee's 9-to-5 vote against Bork last week, hedged his negative vote by saying it was proper "at this time and at this posture of the confirmation process."

In an interview with CNN, Reagan named Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.), and two other committee members, Sen. Edward M. Kennedy (D-Mass.) and Sen. Howard M. Metzenbaum (D-Ohio), as the "three principal leaders" in what he called a campaign of lying and distortions about Bork "that actually amount to a lynching."

The president also used his weekly radio address yesterday to promote the Bork nomination, praising Bork's "courage" for seeking a full Senate vote. The awkward situation of calling for support of Bork when the nomination appears certain to fail was reflected in the tone of Reagan's radio talk. He offered sympathy for Bork and used the kind of language that he has often reserved for those who have been defeated.

"I felt that he {Bork} had already won an important victory" by making his case for judicial restraint in nationally televised confirmation hearings, Reagan said.

In the television interview, conducted Friday, Reagan conceded that Bork now lacks votes for confirmation. "I know," he said when told that the numbers do not add up to confirmation.

Reagan quickly named Biden and Kennedy but had trouble in the interview remembering the name of the third senator he accused of leading the "lynch mob," Metzenbaum.

Asked who within the White House "screwed up" the Bork nomination, Reagan said, "I don't think anyone did." He went on to blame the Democratic-controlled Congress, saying his major accomplishments had come in the six years when the Senate was in Republican hands.

Even as the administration remains officially committed to Bork, Justice Department lawyers are researching other candidates. Among those being discussed as contenders are federal appeals court judges Pasco M. Bowman II of Kansas City, J. Clifford Wallace of San Diego and Patrick E. Higginbotham of Dallas.

Others who have been mentioned as possibilities include Laurence H. Silberman and Douglas H. Ginsburg of the federal appeals court here; Roger J. Miner and Ralph K. Winter, judges on the 2d U.S. Circuit Court of Appeals; Frank Easterbrook of the 7th Circuit in Chicago, and Edith H. Jones of the 5th Circuit in Houston.

"In light of what we've gone through, you've got to make a strategic decision about who we're going to put up," another Justice Department official said. Administration officials are split over whether to choose another nominee as conservative as Bork or a "consensus candidate" who would not provoke another fierce confirmation battle, sources said.

Another Justice Department officials noted that "the delay also gives us a chance to look more carefully at a broader range of candidates, and that's not all bad."