Auxiliary Bishop Thomas W. Lyons, 56, has been named apostolic administrator of the Roman Catholic Archdiocese of Washington, a sort of charge d'affairs for the archidiocese until a successor to Cardinal William W. Baum is chosen.

Although Baum was named to a high Vatican post more than two months ago, he did not formally resign as head of the local archdiocese until a few days ago.

His resignation now opens the way for the Apostolic Delegate, Archbishop Jean Jadot, to begin formal consultations with lay and clerical leaders over the choice of a successor.

Lyons born and educated here, has spent his entire church career in the Washington archdiocese. He was made an auxiliary bishop in 1974.

There have been no indications when a new archbishop for Washington will be designated by the Vatican. In St. Louis, an archidiocese of comparable significance to the church in this country, the Most Rev. John May was recently named archbishop -- seven months after the retirement of Cardinal John Carberry.

Following guidelines laid down by the Vatican in 1972, Jadot will solicit suggestions from dozens of Catholic leaders here for a slate of three candidates to be proposed to the Vatican for a final decision. "The archbishop is committed to completing the process in as reasonable a time as possible," an aide said yesterday.