Not much has changed since mid-January, when we last addressed the unpleasant prospect of another prison for the District of Columbia -- except for Mayor Barry's sudden discovery of lots of prisoners, whom others in and out of Lorton have been citing all along as evidence that something's got to give to accommodate everybody. Now, with an offer of federal financing and possible federal land on which to build, Mayor Barry is formally on record in support of the project -- and his decision is a good one. No matter how creative the local administration may become in coming up with alternative facilities and programs for certain categories of lawbreakers, new prison space remains a must.

Besides, this is one of those offers that doesn't come every year. Sen. Arlen Specter of Pennsylvania, who heads the Senate's Appropriations subcommittee on the District, has been spearheading the move; and the Reagan administration is backing it. In the meantime, the numbers of arrests and incarcerations have been rising constantly and rapidly; on Tuesday, Lorton had about 80 more inmates than it is rated to hold, and the D.C. Jail had about double the population it was established to hold. In all, the number of people incarcerated has increased by 6.3 percent since December.

Mayor Barry also has emphasized that the new facility should be in the District of Columbia. D.C. Council Chairman David A. Clarke, on the other hand, has said any new facilities should be at the Lorton complex in Virginia. Mayor Barry is right. If federal land exists in the District, there is no good reason to expand in Virginia. The idea is not supposed to be to farm out criminals to other places. Lorton remains a necessary and proper facility, and it is not about to be closed or relocated. While suburban politicians love to take cheap shots at this city facility in their midst, they would have a legitimate complaint if the city ignored offers of in- city federal land and built more in Fairfax County instead.

It is true, as one spokesman for a prison project said, that "putting money into more bricks and mortar won't solve the crime problem." The city administration has been studying prisoner profiles to determine who might be released safely and/or put into other programs; and leaving aside absurd suggestions to let burglars and gun-toters run free, this approach is valuable. But as long as existing jails and prisons are overcrowded, relief has to include the addition of more space.