The Pentagon faces at least one congressional investigation of its draft directive that would authorize wider use of lie detectors among its 3 million employes, defense contractors and, upon request, government workers in other departments.

Rep. Don Edwards (D-Calif.), chairman of the House Judiciary subcommittee on civil and constitutional rights, has said he will conduct an inquiry on implications of the directive.

A lawyer, former FBI agent and Navy intelligence officer and a member of the national commission that investigated wiretapping and electronic surveillance in 1974, Edwards wrote Defense Secretary Caspar W. Weinberger Friday to express reservations about wider use of polygraphs.

"Involved in the issue are fundamental rights inherent in and guaranteed by the constitutional provisions of the First, Fourth and FifthAmendments . . . . The purpose of this letter is to urge you strongly to delay any change in Pentagon polygraph rules until there have been hearings by the appropriate congressional committees . . . ," he wrote.

"There is substantial evidence" that widening use of polygraphs "would be a serious mistake. If there is a real security problem faced by the Pentagon, then the extent of that problem should be outlined in congressional testimony," the letter said.

Besides Edwards, Senate Assistant Minority Leader Alan Cranston (D-Calif.) is considering requesting hearings on the Pentagon's draft polygraph directive, according to an aide.