BILLY CARTER, who requested the forms necessary to declare himself a legally registered foreign agent for the government of Libya three months ago and then never filled them out, is now under active investigation by the Justice Department for failure to do so.

Joel Lisker, chief of the Foreign Agents Registration Act section, began openly calling potential witnesses last week and making appointments to interview them with their attorneys.

A Justice Department spokesman said yesterday that they would have "no comment" to make on the escalated investigation, which has been rumored for weeks to be progressing delicately along very discreet lines of inquiry.

The president's brother, who visited Libya twice this year as the guest of dictator Muammar Qaddafi, wrote to the Justice Department in August asking for registration forms, just as he was preparing to leave for Tripoli to celebrate the 10th anniversary of the military coup.

By strictest interpretation of the law, Carter had 10 days after his return to file his declaration if he decided to become Col. Qaddafi's representative. The question now is whether or not Carter acted as an agent without having filed.

Some violations of the Foreign Agents Act can be misdemeanors, punishable by a fine of up to $5,000 and/or up to six months in jail. Other violations of the Act are considered felonies punishable by a fine up to $10,000 and/or imprisonment of up to five years.

Billy Carter started making headlines with the Libyans last January when he escorted a high-level delegation on a 10-state tour of the U.S.

The Libyan government had been so eager to cultivater Billy's friendship that a special envoy was dispatched to Georgia in advance of the trip to find someone in Atlanta who knew him well enough to make the necessary introductions. A "good ol' boy" friend of Billy's agreed to act as liaison and drove the Libyan diplomat to Plains in his Winnebago camper to make contact.

Carter and the Libyans hit it off so well that one of his associates was telling neighbors in Plains and Maericus that the two of them were "going to buy us an oil tanker."

One of the potential witnesses with whom Justice made contact last week was Clare Francis Stahl, who did more than just act as social liaison for the Libyan delegation here. Stahl, who staged a $20,000 Libyan party for Billy at the Madison Hotel here last February, also did the logistics for both his first-class, all-expense-paid trips which together reportedly cost somewhere close to $100,000.

Stahl has already told Lisker that the Libyan Embassy deliberately falsified State Department customs documents in order to get a $10,000 silver saddle that had been a gift to Billy Carter during his first visit admitted to the U.S. duty free.

Stahl says that the Protocol Office at State had refused three time to approve the saddle's delivery. Then she personally filled out a form stating that the saddle was intended to be used permanently as a decoration in the ambassador's office. The form was stamped with the embassy seal, she says, and the saddle was picked up and sent to Billy in Georgia.

Stahl told Justice that she had been ordered to falsify the document by Libyan embassy officials who stood over her "shaking their fists" at her inability to cut her way through what they considered bothersome red tape. She said she did it "under duress."

Stahl and her lawyer, David Dulles, nephew of the late Secretary of State John Foster Dulles, were scheduled to meet with Lisker next week.

Lisker's list of potential witnesses also reportedly includes Chicago-based public relations man Maurice Starks.

Starks, who represented Uganda's "Big Daddy" Amin, picked up the Libyan account here over an hor d'oevres tray during a reception at the Ugandan Embassy.

Anyone who was good enough for "Big Daddy" Starks later told a reporter, was good enough for Qaddafi.