President Carter expressed "full confidence" yesterday that a federal investigation into the finances of budget director Bert Lance would be handled "properly" by Lance and the Office of the Comptroller of the Currency.

But in answering a three-part question about Lance at his welfare news conference, the President did not respond to a part that asked ". . . does he still have you full confidence?"

The comptroller's office, which regulates all nationally chartered banks, is investigating whether Lance improperly used interest-free bank deposits from National Bank of Georgia, which he headed, to induce a New York bank and a Chicago bank to grant him large personal loans.

Lance called a press conference late Friday to say that he had done nothing imporper in obtaining a $2.6 million loan from New York's Manufacturers Hanover Trust Co. in 1975 and a $3.4 million loan from First National Bank of Chicago in late 1976.

In both instances, Lance's National Bank of Georgia established correspondent relationships with the New York and Chicago banks just about the time Lance received the personal loans.

In correspondent relationships, smaller banks receive a variety of services from big banks, such as check clearing, loan participation arrangements, management or accounting advice, and training programs. Instead of paying for these services, the smaller banks generally maintain correspondent balances, or deposits, with the bigger bank on which they earn no interest.

At issue is whether these correspondent balances were somehow tied to Lance's personal loans. In some cases that could be illegal. An official close to the investigation said yesterday that it did not appear Lance had done anything criminally wrong.

Lance said that the loans he received were not related to the correspondent relationships the National Bank of Georgia established and that the terms of the loans were standard.

But Lance acknowledged to reporters that investigators for the comptroller's office had discovered in the New York bank's files a memo written the same day the bank approved Lance's $2.6 million loan that appeared to link the size of the interest-free account his bank had to maintain to the personal loan he received.

The April 24, 1975, memo said that National Bank of Georgia would be expected to keep an account equal to 20 per cent of the "facility." Both Lance and Manufacturers Hanover vice president James Hambleton said they did not know what the word "facility" referred to.

Generally when barkers refer to a "facility" they mean the amount of a loan or line of credit.

C. Westbrook Murphy, deputy comptroller of the currency, said that upon completion of the investigation - which he said is "days" away - his agency will make public all the information it has about the loan. President Carter said the same thing at his morning news conference in Plains, Ga.

The President said he became aware of the comptroller's inquiry "a week or 10 days ago . . . I have not talked to Mr. Lance about it."

A source close to the investigation said Lance has told investigators, including the new comptrolier of the currency, John G. Heimann, with whom he met Friday, that he did nothing improper in arranging personal loans with the same institutions that held correspondent balances with the bank he headed.

"Everyone does it," Lance is reported to have said several times.

Officials said it is common practice among top officers in the South and Southwest but rare elsewhere. One federal official suggested the Lance episode will lead to major changes in banking laws, specifically on borrowing by bank officers and compensating balances. A compensating balance is an interest-free deposit a borrower is required to maintain at the lending institution as a condition of the loan.

Lance used the proceeds of the Manufacturers Hanover loan to buy stock in National Bank of Georgia and used the First Chicago loan to pay off the New York bank and buy more shares of NBG. Lance is now in the process of selling the NBG stock.