Shares of the National Bank of Georgia - the bank in which federal budget director Bert Lance holds a major stake - jumped 1 1/6 points today even though the bank today reported a $1.4 million second quarter loss.

The stock had gained three quarters of a point on Tuesday.

The increase to a price of $11.25 bid and $12.25 asked in the over-the-counter market was attributed to President Carter's efforts to free Lance from his commitment to liquidate the 190,000 National Bank of Georgia shares he owns by the end of the year. It had been trading as law as $850.

President Carter on Tuesday asked the Senate Government Affairs Committee to waive the deadline which had been part of the administration's conflict-of-interest rule because he said it put an "undue financial burden" on Lance as well as the other bank shareholders.

Lance bought the shares in 1975 and 1976 at about $17 each, financing the purchase with a bank loan.

Today's loss report had been expected after NSBG president Robert P. Guyton, who replaced Lance as the bank's chief executive officer, announced that the bank would have to take $2.3 million in write-offs on problem loans in the second quarter.

The second quarter loss of $1.42 million ($1.14 per share) before securities transactions compared with a profit of $395,000 (49c a share) in the same period last year and put the bank into the red by $1.39 million for the year to date.