It took some heavy, last-resort pressure by a court to force city hall into serious action on its prison/jail mess, but Mayor Barry has responded strongly. He's succeeded in staving off the court appointment of a "special master" to run a city prison facility, by naming his own special assistant who is highly qualified for the task. Fifteen years of city foot- dragging is what had prompted U.S. District Judge June L. Green to call for an independent master to monitor Lorton Reformatory's Central Facility. While putting the court into the business of running prisons didn't appeal to us, clearly some drastic action was in order -- and Mayor Barry's choice of retired Superior Court Judge John D. Fauntleroy was good enough for Judge Green to postpone her action for at least six months.

But hold the applause until there's a measure of the city administration's commitment to improve things. For now, at least, the attorney for the inmates at Central says he believes Mr. Barry's personal commitment, along with Judge Fauntleroy's personal integrity, could produce better and quicker results than a court-ordered master. Judge Fauntleroy is to have "unlimited access" to the mayor, city officials, Judge Green and inmates' attorneys; and he will have help from a new corrections expert to be detailed to him.

This is the golden opportunity to put all the pieces of the prison/jail issue together -- and we submit the following matters for consideration by Judge Fauntleroy:

Mayor Barry's pledge to build a new prison in the District must not be allowed to flag for any reason. He's on record for it, he has suggested sites for it, and the Justice Department should give the go-ahead. There could and should be a deadline for getting construction plans under way, and September strikes us as not a moment too soon.

Using all the influence that Judge Fauntleroy has, the city should continue to press the Justice Department to resume accepting D.C. inmates at federal prisons. Even Fairfax County Board of Supervisors Chairman John F. Herrity -- who has had more than a few battles with Mr. Barry about Lorton -- has joined the mayor in an appeal to Justice. If the Reagan administration is serious about helping, the federal government should agree.

If every agency involved is to continue doing its job as pledged -- police arresting suspects, prosecutors seeking convictions, and judges sentencing convicts -- there needs to be some understanding of exactly what is to be done to avoid exceeding inmate ceilings. Judge Fauntleroy could call together all parties to reach some understanding of how to expand the number of facilities on a temporary basis.

Judge Fauntleroy can't be expected to work political miracles in a situation that is as complex as it is old in this city. But the presence and the recommendations of a respected and clearly concerned member of the bench could be the impetus for some serious and long overdue improvements.