The Federal Reserve Board yesterday complicated Budget Director Bert Lance's finances, putting the National Bank of Georgia stock he is trying to sell on its list of over-the-counter stocks that are subject to margin restrictions.

That means that starting today only 50 per cent of the value of the stock can be pledged as collateral on a loan.

The Fed adds stocks to its margin list when they begin to exhibit characteristics of securities traded on stock exchanges, according to retired Princeton economics professor and banking expert Lester V. Chandler.

The margin regulations are designed to restrict speculations in bank stocks and apply to all stocks listed on exchanges - as well as to over-the-counter stocks the Fed determines to be traded widely enough to be on its margin list.

The Fed action does not affect the $3.4 million loan Lance has with the First National Bank of Chicago in which his 200,000 shares of National Bank of Georgia stock are the major portion of the collateral.

But Lance, through a trustee, is trying to sell his shares of NBG stock by the end of the year as part of an agreement he reached with the Senate Banking Committee at his confirmation hearings last winter.

And the two potential buyers of the Lance stock - Atlanta businessman David N. Smith and Tennessee businessman Franklin Haney - could be affected.

Before yesterday's action, these two buyers could have put as little down to buy the stocks as a lender would permit. Starting today, anyone buying National Bank of Georgia stock on credit must make a downpayment equal to 50 per cent of the value of the stock.

About 1,100 stocks are on the Fed's margin list, which the agency revises several times a year. In the revision announced yesterday, the central bank added 195 stocks to the list, removed 13 because they failed to be traded widely and took another 43 off because they have been listed on a national securities exchange.

Some large, well-known companies are traded over-the-counter - that is, are not traded on an exchange - such as Anheuser-Busch, Inc., Government Employees Insurance Co. and Kaiser Steel Corp.

Lance, who heads the Office of Management and Budget, is the subject of an investigation by the Comptroller of the Currency, who is trying to determine whether Lance used interest-fee deposits from the National Bank of Georgia, which he headed until early this year, to induce a New York bank and the Chicago bank to make him large personal loans.

Lance established a correspondent account with Manufacturers Hanover Trust of New York in late 1975 just about the time the bank granted him a $2.4 million loan to buy National Bank of Georgia stock. Last December he received a $3.4 million loan from First Chicago. He used that loan to pay off the New York bank and buy more shares of NBG stock. A month later he pledged to sell the stock by the end of 1977.

If Lance's trustee sold the stock today on the open market Lance could lose as much as $1 million. This is because the bank's stock has declined in value as the institution reported losses in recent months and then announced last week it would cancel its quarterly 20-cent dividend. Lance relied in part on his $160,000-a-year in dividends to keep up payments on his loans.

The potential buyers of Lance's stock, however, apparently are willing to buy the stock at a price over current market value.