April 22, 1981

An internal Justice Department report on the handling of the Billy Carter case has concluded that no Government official violated the law in the department's investigation of Mr. Carter's relationship with Libya. However, the report, prepared by Michael E. Shaheen Jr., head of the department's Office of Professional Responsibility and made public today, asserts that Text of the report is on page A21. the brother of former President Jimmy Carter ''lied to Government agents'' investigating his responsibility to register as an agent of the Libyan Government and recommended that the criminal division of the department decide whether he should be prosecuted. No Illegal Conduct Found ''Our primary conclusion is that no Government officials or employees have been shown to have engaged in illegal conduct,'' Mr. Shaheen said in his 10-page final report, submitted to the Solicitor General, Wade H. McCree Jr., who said he agreed with the findings.

Joe Louis, the sharecropper's son with the knockout punch, was buried in Arlington National Cemetery today, cherished in farewells at the grave and remembrances on the street corners as the ultimate champion who smashed the myth of racial supremacy. Three rifle volleys were fired across Louis's bronze-toned coffin as a crowd of several hundred watched the family and a gathering of boxing celebrities bid goodbye at Louis's open grave. The words of the New Testament saw him to rest: ''I have fought the good fight. I have finished the race. I have kept the faith.''

FOR those who dine in better restaurants, the problem is getting a reservation. But the people who run the good restaurants say that is nothing compared with their problem: People who make reservations and then, without bothering to cancel, do not show up. A check of dozens of Manhattan restaurants found that the problem had become so bad recently that many had taken drastic steps in an effort to counteract it. These measures vary according to the nature of the restaurant and its business and to the day of the week.

Shareholders paid a fond farewell yesterday to David Rockefeller, who retired as chairman of the Chase Manhattan Bank and its corporate parent, the Chase Manhattan Corporation. Mr. Rockefeller was given a one-minute standing ovation at the bank's annual meeting in honor of his 35 years with Chase, including 12 as its chairman. Mr. Rockefeller, at 65, has reached the mandatory retirement age. But Willard C. Butcher, the former president who succeeded Mr. Rockefeller as chairman, surprised the audience when he announced that Mr. Rockefeller had been named chairman of Chase's international advisory council, a prestigious group that meets twice a year and advises the bank on international matters.

The Going Out Guide yesterday incorrectly listed a performer appearing this week at Sweet Basil, 88 Seventh Avenue South. The correct performer is the trombonist Kai Winding.