Jury selection in the criminal conspiracy and bank fraud trail or former budget director Bert Lance and three others began today at U.S. District Court here after the defendants were blocked in an 11th-hour effort to delay the trail.

The bid for a delay was based on the contention of prosecution leaks of grand jury deliberations to the press. In denying the motion for a stay, U.S. District Judge Charles A. Moye Jr. said: "This court finds the paramount public interest to require the speedy trail of this case."

Lance and the others were charged May 23 in a 33-count indictment alleging by conspiring to obtain about $20 million in illegal loans.Lance, 48 resigned in September 1977 as director of the federal Office of Management and Budget after news accounts and regulatory probes raised questions about his financial dealings while he was a Georgia banker.

On trail with Lance and Thomas M. Mitchell, 44, who handled Lance's business affairs while he was in Washington; Richard T. Carr, 43, a onetime banking associate of Lance, and H. Jackson Mullins, 49, a former druggist in Lance's hometown of Calhoun, Ga., who allegedly lent his name to a variety of Lance's financial manipulations.

Declaring "I'm ready to go," Lance pushed his way though a phalanx of reporters and television cameramen this morning for the most publicized prosecution of a public figure since Watergate.

Lance's wife, LaBelle, grasped his hand, and three of their four sons trailed them into the courthouse. Jury selection is talking place in the massive ceremonial courtroom to accommodate the 120 prospective jurors.

The would-be jurors were sent questionnaires to speed up the selection process in a case in which both sides agree that it would be difficult to find an unbiased jury.

The 120 members of the panel were not told until today that they might be on the Lance jury. A murmur went through the group when the hulking 6-foot-5 Lance entered the courtroom.

This is the first case to be heard in the federal court in the new Richard B. Russell federal building, named after the late U.S. senator.

Moye said final selection of the jury of 12 members and six alternates will take place as soon as 56 members of the 120-person panel go unchallenged. The two sides passed on eight of the 56 today.

The potential jurors were queried about their financial affairs, their familiarity with the lance case and whether they had read LaBelle Lance's book about the affair, titled "This Too Shall Pass."

The complex appeals process based on the alleged grand jury leaks began in March when the defendants sought civil sanctions, alleging the prosecutors had leaked grand jury information to the press. U.S. District Court Judge Richard Freeman refused to grant a hearing on the petition.

The defendants appealed Freeman's decision to the 5th U.S. Circuit Court of Appeals in New Orleans. A week ago that court reversed Freeman's decision and ordered him to hold a hearing on the allegation of news leaks by the prosecutors.

But yesterday, Freeman said he saw no reason to convene a hearing on the civil question until the criminal trail was completed."We emphatically resist any course that could interfere with [the] trail," Freeman said. The defendants immediately appealed again to the 5th Circuit, which denied their request for a speedy hearing.

After the same time, Moye turned down the separate request to have the criminal indictment dismissed on the ground that the alleged leaks biased the grand jury.