The government today portrayed former budget director Bert Lance as the mastermind of a multibank, $20 million criminal fraud scheme devised to enrich himself, associates, family and friends.

"The doors of the vaults of a number of banks were opened . . . if you were a friend, associate or business partner of Mr. Lance," Justice Department attorney Marvin R. Loewy said.

In a 90-minute opening statement at U.S. District Court here, Loewy explained how the government plans to prove that Lance and three codefendants committed bank fraud and conspiracy, as spelled out in a 33-count-indictment returned in May.

Loewy alledged that banks have been forced to write off $750,000 of the loans they made to Lance and others -- about a quarter of a million dollars more than stated in the indictment.

Attorneys for Lance and his three codefendents are to present opening statements Wednesday.

A federal grand jury on May 23 charged the four defendants with violating U.S. banking laws in an intricate conspiracy to obtain 383 loans from 41 financial institutions beginning in 1970 and continuing well after Lance resigned from the Carter administration in September 1977.

On trial with the 48-year-old Lance are his former trustee, Thomas M. Mitchell, 44, who handled Lance's business affairs while Lance was in Washington; Richard T. Carr, 43, a onetime northwest Georgia banking associate of Lance, and H. Jackson Mullins, 49, a druggist in Lance's hometown of Calhoun who allegedly lent his name to a variety of Lance's financial manipulations.

There are seven blacks and five whites on the six-man, six-woman jury. Members include an auto worker, a nurse, a railroad porter and a seamstress.

The defense apparently favored jurors uninitiated in high finance. At one point last week, chief prosecutor Edwin J. Tomko sought unsuccessfully to have three members of the current panel excluded from the selection process because he argued, they "lacked even the most fundamental background" to follow the intricate financial case.

Loewy today sought to compare normal banking affairs with the allegedly privileged deals struck by Lance and the others.

"Even bank presidents like Mr. Lance and Mr. Carr cannot under the law use depositors' money as if it were their own." Loewy told the jury.

During the period covered by the government's case, Lance was president of Calhoun First National Bank and the National Bank of Georgia in Atlanta. Carr was president of Northwest Georgia Bank in Ringgold.

Loewy opened his statement as if telling a story. "One day in the town of Calhoun," he began, relating how on Dec. 31, 1976, Lance owed $140,000 to the Trust Co. in Atlanta. To pay this, Lance allegedly wrote a check for $140,000 on the Lancelot Co. account at the Calhoun bank.

But Lancelot was simply a "shell" company formed by Lance and his wife, and lacked assets, the government contended.

To cover the check, Lance then wrotea check on an account at NBG, where he was also president, the government said, adding there was no money to cover this check either. That overdraft was covered when Lance got a $3.5 million loan from First National Bank of Chicago, which the government claims that was "based on a false financial statement" given to the bank by Lance.

Loewy said the government will show how Lance realized that depositors from Tennesse were putting their money into banks in northwest Georgia because of high interest rates there. As part of the conspiracy to get at the assets of those banks, the government contends that Lance arranged for Carr to be president of the Ringgold bank, one of the richest. And Mitchell was on the board of that bank and several others for the same purpose, it contends.

"We see Mr. Mitchell as a front for Mr. Lance," Loewy said.

The government claims that Carr, who earned only a modest salary from the bank, "falsely claimed" a net worth of more than $900,000 in order to borrow from various banks from personal investments, including stock in several of the northwest Georgia banks.

Mullins also borrowed beyond his means, the government said.

The government contends that the defendents wrote overdrafts on their various bank accounts to help pay these loans and sometimes to cover their earlier overdrafts.

Loewy claimed that the four defendants worked "together as coconspirators to get money from these banks that they couldn't have gotten if they were ordinary people."

All four of Lance's sons were in court today, and Loewy, in his remarks, told of how in 1973, when a federal bank examiner questioned a $45,000 unsecured loan from the Calhoun bank to Lance's son David, then 18, Lance replied: "Just because David's a college student, he doesn't have to live like a pauper."

As Lance was leaving court, he characterized the prosecution's statement as the "same old stuff. I've heard it all before. I know the truth, and you know what they say, the truth shall set me free."

In another development today, defendant Tom Mitchell was reelected to the state Transportation Board by a caucus of state legislators.