Bert Lance was acquitted today on nine counts of bank fraud. A mistrial was declared on three other counts because the federal court jury was unable to reach a verdict after eight days of deliberating.

Lance, President Carter's first budget director and once one of his closest confidants, said he was delighted. His wife, LaBelle, burst into tears. Their sons gathered around to offer congratulations.

The former Georgia banker and his lawyers, however, seemed somewhat subdued, perhaps because they had failed to win the complete vindication they had sought. Most of the jurors had voted to convict Lance on two of the three charges that were left unresolved.

U.S. District Court Judge Charles A. Moye Jr. gave defense attorneys until May 20 to submit briefs on their motion for directed verdicts of acquittal on the three counts. He gave the government until June 10 to reply and, in effect, to decide whether it wants a new trial.

Several of the jurors indicated that the key to their decision involved doubts that Lance and his three codefendants had really intended to defraud the banks where they obtained more than $20 million in loans for themselves, their families and friends.

As juror James Collins of Blue Ridge, Ga., told reporters: "Even if something happened, could you say they intended to hurt somebody?"

As the jurors filed from the courtroom after the verdict, some of them smiled and waved to Lance and his codefendants. The one defendant acquitted of all charges, Thomas Mitchell, who was Lance's trustee while Lance was budget director, blew kisses at the jury. Lance and the two others, Richard T. Carr and H. Jackson Mullins, waved goodbye.

Throughout the trial, Lance's lawyers portrayed him as a man who could be trusted, a country banker "who made loans on the basis of a borrower's character, not his collateral."

After the verdicts today, Lance told a crush of reporters outside the federal building here: "We're delighted at the outcome. But we knew it all along."

The criminal investigation that led to Lance's indictment last year began in September 1977, when he was forced to resign from the Carter administration in light of questionable financial dealings when Lance headed the Calhoun, Ga., First National Bank and the National Bank of Georgia in Atlanta.

Lance and his three codefendants were eventually indicted in May 1979 by a federal grand jury here on conspiracy charges and 32 other counts involving 383 bank loans.

During the 3 1/2-month trial, however, Moye trimmed back the indictment sharply, first tossing out the broadly drawn conspiracy charge, with which the government had tried to tie the case together, and then eliminating more than a dozen other counts.

By the time the case went to the jury, there were 12 criminal counts against Lance, all of them felonies, still to be settled. The jurors were deadlocked on three of them. One alleged that Lance had misapplied $12,000 in bank funds, and the other two accused him of filing false financial statements to get a $175,000 bank loan.

The jurors also failed to reach any agreement on three of the six remaining counts against Carr and one of the four remaining counts against Mullins.

On Tuesday night, jury forewoman Marian Foster sent out her third note in as many days to report no progress toward a unanimous verdict on every count. At that point, Moye apparently concluded that further deliberations would be fruitless.

William M. Savage Jr., 36, a carpenter from Lawrenceville, Ga., and several other jurors said the jury had voted 10 to 2 to convict Lance on a charge that he had submitted a false financial statement June 27, 1975, to get a $175,000 loan from the Trust Company Bank of Atlanta.

But the jurors also voted 10 to 2 to acquit Lance of another charge of deliberately making a false statement a year earlier, on July 5, 1974, in connection with the same $175,000 loan.

"Some of us thought that the first one was a mistake by Lance," Savage explained.

The government contended that Lance had concealed more than $1 million in debts that should have been reported on his statements to the Trust Company Bank.

The other unresolved count against Lance involved a $12,000 loan from the National Bank of Georgia that he arranged for Carr when Carr already had more than $500,000 in debts. According to those interviewed, the jury voted 8 to 4 to convict both Lance and Carr on this charge.

Savage said the first day or two of the jury's deliberations were "rough" because of a series of arguments among the jurors. Savage said he wanted Lance acquitted on all counts from the outset of the deliberations. He allowed that "there were a couple of counts I wasn't sure of, but as long as I wasn't sure, I voted not guilty."

Juror Collins, who plays guitar in a country band, said the complexity of the case had "definitely" hurt the government. Another juror, Eloise Hutchins, an Atlanta housewife, said she found Lance, who testified in his own behalf, to be a "man of character" -- the same phrase that defense lawyers had used repeatedly to describe Lance during the trial.

Defense lawyers had expected a not guilty verdict the first day the case went to the jury, but both they and the jurors credited chief prosecutor Edwin J. Tomko's final summation for pulling the case together and making it tougher to decide.

Immediately after the verdicts were announced, Tomko went over to Lance and shook his hand. Later, Tomko said, "I'm a little disappointed. Everybody wants to win."

Another Justice Department lawyer, Marvin Loewy, said he thought "the odds are pretty good for a new trial" on the unresolved counts. Most of them involve allegedly false statements to various banks by Lance. Carr or Mullins. "False statement counts are clean ones to try," Loewy said.

For his part, Lance called the investigation and trial a "total and ridiculous waste of taxpayers' money." He said he has "no plans" to return 'to public life. For now, he said, "we're going to get some rest."

Lance spoke by telephone with Carter after the verdicts. He said the president reminded him of an occasion nearly three years ago when Carter was taken to task for saying "Bert, I'm proud of you," while Lance was under investigation. Carter told him today: "I'm still proud of you," Lance said.