The Senate subcommittee investigating Billy Carter apparently has resolved a backstage dispute with the White House over documents deemed essential to the inquiry.

Although President Carter had pledged full cooperation with the investigation, Sen. Irch Bayh (D-Ind.), the subcommittee chairman, said yesterday that some White House aides turned out to be "more anxious to protect the president than he has been to protect himself."

Bayh said he was confident now, however, that "all the problems have been resolved with the White House."

Senate lawyers dickered inconclusively with White House counsel last week over the subcommittee's original requests for "all" White House documents involving the president's brother and Libya. Finally the subcommittee's attorneys delivered what some sources call a "final demand" Friday, narrowing their requests to a fairly specific list of records.

White House special counsel Alfred Moses agreed Tuesday to comply after some final quibbling over wording, sources said. Moses wanted assurance, these sources said, that only relevant "portions" of some documents were being sought.

Despite the agreement, the documents have yet to be supplied. as a result, Bayh said yesterday, the public hearings originally set for next week to take testimony from White House witnesses are likely to be delayed a week.

"We want the documents before we do any serious questioning of the witnesses," even in preliminary interview, said one Senate source.

Some Senate sources familiar with the investigation had suspected that the White House was stalling deliberately, especially, these sources said, since the subcommittee's original requests for records on July 29 had been met by every other governmental agency other governmental agency on the list.

In other developments after an executive session of the Senate subcommittee yesterday afternoon, Bayh said:

The subcommittee is negotiating with lawyers for Libyan officials here about testifying on Billy Carter's work as a foreign agent for the government of Col. Muammar Qaddafi.

The president's old confidant and first budget director, Bert Lance, will be questioned by Senate Lawyers "within the next day or two" concerning his contacts with foreign bankers about Billy Carter's activities.

The president will be asked to testify before the subcommittee only if it is necessary "to ask him to go through the ordeal." Bayh said he has not made up his mind about that.