THE LANCE AFFAIR is now turning into the Chinese water torture. Each new drop of information about those Georgia banks adds to the administration's embarrassment. But none of them is, by itself, sufficiently dire or shocking to force Bert Lance immediately out of his job as budget director.

That has made the press coverage a major element in the case.Half an inch under the formal defense of Mr. Lance there runs a strong and bitter resentment of news reporting that the White House sees as persecution - a malicious attempt to hound Mr. Lance out of office for the sheer sport of it. That view, demonstrably, draws great support in Congress. "I think we've gone completely ethics-happy around here," Sen. John Glenn (D-Ohio) exclaimed at an earlier stage of Mr. Lance's troubles. To form a judgment, it's useful to recall where the present imbroglio came from, and where it seems to be going.

In January, as a condition of his confirmation, Mr. Lance promised the Senate Government Affairs Committee that he would sell his bank stock by the end of the year. In late May, Time magazine reported that the sinking price of the stock was exerting a new financial pressure on Mr. Lance. Nothing happened. One Monday in mid-July, Newsweek magazine appeared with a story carrying more details and mentioning Mr. Lance's overdrafts at one bank of which he was president. On the following day, President Carter asked the Senate committee to release Mr. Lance from his promise to sell the stock by the end of the year in view of the great loss that he would sustain. That unexpected request suddenly gave great weight to the magazine articles, and that is the point at which other publications - including this one - began taking a closer look at Mr. Lance's position.

A week later, the Government Affairs Committee summoned Mr. Lance to a hearing at which it extended a sweeping acquittal to him and denounced his accusers. "You have been smeared from one end of the country to the other, in my opinion unjustly," the chairman, Sen. Abraham Ribicoff (D-Conn.), told him. But at that hearing it also developed that the Comptroller of the Currency was looking into Mr. Lance's affairs.

The President and Mr. Lance made a genuinely serious mistake when the Comptroller's report appeared on Aug. 18. They would have been wiser to acknowledge that Mr. Lance had done much that he ought not to have done. When they claimed to see no blemishes in his record at all, each blemish at once became a public issue - and, of course, a news story. The White House keeps challenging the world in general to cite any evidence of illegality, or even impropriety. But the Comptroller's report contains some of each. It notes 50 personal loans to Mr. Lance that he was required by law to report to the bank regulators.He did not. That's not a criminal offense, but it is a violation of the law or, more accurately, 50 violations of the law. As for impropriety, there is that pattern of large, sustained and repeated overdrafts in his and his relatives' accounts in a bank that Mr. Lance was running. The Comptroller called it"unsafe and unsound" banking. But a week after the Comptroller's report appeared, Mr. Carter again told a press conference, "I don't know of any allegation that has been made, or proven, that Bert Lance did anything illegal or even enethical."

The Comptroller's report offers an unflattering view of two banks, but that will mainly be of interest to the people who write and enforce the banking laws. As for Mr. Lance, he is an ingratiating figure who is nobody's idea of a villian. The larger public interest here goes one level higher. It was the President's intercession for Mr. Lance to get the stock requirement waived that brought the present extensive press coverage to Mr. Lance's banks and his finances. It is the Comptroller's report, not the news stories, that now constitutes the authoritative source of information and judgment.

Mr. Carter has reacted as though he sought to dispel this challenge to his close friend and adviser by an effort of sheer will. But government doesn't work that way. Anything that the President touches will draw the close attention of multitudes of citizens who want to know how their government is being run, and by what rules.

The Lance affair is important not for what it tells the country about Georgia banking, or about one Georgia banker, but for what it tells about the Georgia farmer who is now President. It now appears that the Comptroller, after writing his report, has sent examiners back to one of the banks for a still closer look. A couple of weeks ago we observed in this space that Mr. Carter could keep Mr. Lance in the White House only at a price. That price now seems to be rising steeply.