Under pressure from Mayor Marion Barry, the D.C. lottery board agreed last January to abandon plans to set up permanent quarters in downtown Washington and to move instead to an office building in Anacostia, to help promote the economic growth of that depressed area.

But since then, efforts to secure a permanent home east of the Anacostia River have stalled, with no indication that the board will soon be able to move out of its cramped, $185,000-a-year temporary quarters on New York Avenue NW.

The site under consideration is a five-story former furniture warehouse at 2101 Martin Luther King Jr. Ave. SE, owned by Curtis Properties Inc.

The lottery board rented the first floor of the warehouse and then sublet it to Lottery Technology Enterprises, the firm hired by the board to operate the daily numbers lottery game. But little else has been done to get the building ready to house the lottery board and its staff.

Edmond Taylor, a Curtis leasing agent, said his firm has agreed to have the building renovated to meet the lottery board's needs, but that the board has yet to specify what work needs to be done.

One effect of the delay might be to give Jeffrey N. Cohen, a prominent Washington-area developer and a key supporter of the mayor, more time to get involved. Chester C. Carter, the lottery board's executive director, said Cohen has informally discussed a proposal for Cohen to lease and renovate the Anacostia property and then lease it back to the city.

Carter said D.C. Department of General Services (DGS) officials suggested he talk to Cohen to get some outside advice on how best to proceed with the project and that Cohen had expressed interest in getting involved. Public Works Director John Touchstone, who heads DGS, said he cannot recall whether he made that recommendation. In any case, Carter says the lottery board will pay for any architectural drawings that Cohen might commission.

If the board does agree to go ahead with renovations, Carter noted, it probably would take at least a year before the building would be ready for occupancy.

Meanwhile, Cohen says the whole deal is pretty iffy. For one thing, he said, he has not decided whether he really wants to submit a proposal. He said he's reluctant to get involved with the lottery board in light of the recent controversy over the manner in which the board awarded major contracts. For now, he says, he's acting chiefly in the capacity of an informal adviser to the lottery officials.

"They the board would like us to make them a proposal because we're good at what we do," Cohen said. "But I frankly don't know if we will."

The bright new "Welcome to Washington" signs bearing Mayor Barry's name that recently appeared at 24 entrances to the city are only a minor example of the large sums of city funds now being spent in the name of promoting tourism.

The signs cost about $4,500, a small fraction of the $703,000 allocated this year for the Mayor's Committee to Promote Washington.

Last week, the committee awarded a $250,000 contract to International Business Services Inc., headed by Marion (Duke) Greene Jr., and Bill Rolle and Associates Inc., to launch an advertising campaign this fall to bolster weekend tourism.

The promotional campaign, largely consisting of newspaper advertising and "entertainment packages," will be designed to lure residents of the New York metropolitan area who may not be aware of all the free cultural entertainment offered in the nation's capital, according to Emily Durso of the D.C. Office of Business and Economic Development.

The committee also awarded a $15,000 grant to provide 32 weeks of culinary training to 24 low-income persons.

Barry administration officials say that the overall promotional campaign is essential to attracting new business to the Washington Convention Center and boosting the local hotel industry, which often has trouble filling its rooms on weekends.

"It the $703,000 annual budget may seem like a lot of money, but L.A. Los Angeles and Chicago spend $3 million to $4 million a year to promote their cities," Durso noted. "The program has finally got the whole hospitality industry to work together . . . and people are focusing on the fact that tourism is the only real growth industry for blue-collar workers."

True enough. But the program, funded with a portion of the proceeds from a $1 per night D.C. hotel occupancy tax, also provides a pool of funds that can serve the traditional political functions of rewarding old allies or courting new ones.

For instance, Abramson Associates, which has served as a campaign media consultant to Barry, has received a $250,000 contract to produce commercials, posters, bumper stickers and other materials to promote the city. The Abramson firm, headed by David Abramson, last year was involved in producing the "Washington Is a Capital City" TV promotion spots.

The mayor's committee also is providing many thousands of dollars in grants to about a dozen neighborhood groups to promote "neighborhood pride."

The funds will be used for such diverse activities as a celebration of the Chinese New Year, the Gay Community Center's "Spring Art '83," a Ward 5 picnic, the 10th Annual Upper Northeast Family Day, and the Adams-Morgan Day Festival.