SINCE WE LAST commented on them, the grey areas in Bert Lance's highly complicated financial affairs have become several shades darker. As President Carter's Director of Management and Budget, his ability to do his job effectively depends on his personal reputation. On Friday, he called a press conference in haste to deny that a certain memorandum, found by federal investigators in the files of a New York bank, meant what it might seem to mean.

The press conference was, clearly, what the military strategists call a preemptive strike. The existence of the memorandum was previously unknown, and Mr. Lance obviously wanted to get the denial into the papers ahead of the revelation. This memorandum had been turned up by examiners for the office of the Comptroller of the Currency, which regulates national banks. On the following day, when Mr. Carter was asked about the affair, he gave a conspicuously cautious answer. He expressed confidence that Mr. Lance and the Comptroller would do the right thing by the investigation and promised that all would be made public. At this point, evidently, neither Mr. Carter nor anyone else is sure that he has the full story.

The Lance case illustrates the possibility that it may not be what an official owns, but rather what he owes, that threatens a conflict of interest. When Mr. Lance became president of the National Bank of Georgia a couple of years ago, he bought a large block of its stock with $2.6 million borrowed from another bank, Manufacturers Hanover in New York. At the same time the Georgia bank put some of its money - initially $250,000, more later - into an account with Manufacturers Hanover that bore no interest.

Mr. Lance says that there was no connection whatever between his personal loan and the no-interest account. The account, he says, was a perfectly customary device to provide the Georgia bank's customers with correspondent services in New York and abroad. But the memo says that there was a connection, and that the Georgia bank was to leave a deposit no less than 20 per cent of Mr. Lance's loan. That part of the case ends, for the moment, in a big question mark.

Last December, after Mr. Lance was nominated to the Cabinet, he moved the loan to the First National Bank of Chicago and increased it to $3.4 million to buy more of his own bank's stock. But in January, as a condition of confirmation by the Senate, he agreed to sell his bank stock by the end of this year. Unfortunately, the price of that stock fell sharply. Its market value amounted to hardly more than half enough to pay off that $3.4 million loan.

Then, providentially, a buyer turned up: a Georgia businessman who was prepared, he said, to pay much more than market value. It is not uncommon for a bid for a stock to be more than the market price, and occasionally quite a lot more if control of the enterprise is at stake. But that explanation does not quite cover this extraordinarily high bid. It is a classic illustration of the ambiguity that dogs the mixing of public and private interests. If the sale goes through, it might well seem to Mr. Lance that he has sold nothing but the stock. The buyer, on the other hand, will have helped a powerful public official out of an excruciating embarrassment. There will be a good many people in the administration wishing the bank the best of luck under its new management, and a quite prosperity that would cease to attract the current unwelcome attention. There does not seem to be any solution to Mr. Lance's troubles that does not leave him in one kind of debt or another to someone else.

It may well turn out that Mr. Lance has done nothing illegal or, for a private businessman, wrong. But that's the point. A difference standard applies to public officials. That memo in New York puts on Mr. Lance the burden of demonstrating that he is not too encumbered to continue serving his old friend the President.