After over a month of delay, a key D.C. City Council committee yesterday unanimously approved Mayor Marion Barry's five nominees to the powerful new D.C. Lottery and Charitable Games Control Board.

The five nominations, which must be approved by the council before the legal gambling operation here can begin, had been stalled since April by Finance and Revenue Committee Chairman John A. Wilson (D-Ward 2), who refused to schedule action on the appointments until he was satisfied that legalized gambling in the city could be properly policed.

It is considered likely that the full council will approve the nominations next month.

Wilson said he decided to move forward with the nominations after Barry and the five nominees agreed to add more money to the lottery board's budget to hire investigators and auditors, slots that were not included in the mayor's original budget proposal.

"I think they're going to need three or four investigators to make sure there's no hanky-panky going on," Wilson said. "I think that their budget needed to be amended, and they agreed to it."

Barry, in his adjustments to the 1982 fiscal year budget, proposed a $628,000 budget for the board to pay for board salaries and benefits, an executive director, a staff attorney, 12 clerical and administrative workers and the price of supplies and start-up costs.

That budget, part of a package of 1982 budget amendments, has been delayed in the council pending resolution of an unrelated matter on Capitol Hill.

The board members approved yesterday are Brant Coopersmith, the retired director of the Washington office of the American Jewish Committee and the chairman of the Citizens Committee that drafted the legal gambling referendum approved by voters last November; Jerry Cooper, the Ward 1 Democratic Club chairman; Lillian Wiggings, a columnist for the Washington Afro-American activist Almore M. Dale, and Carolyn B. Lewis, chairwoman of the D.C. Commission on Women.

Coopersmith, as chairman of the board, would serve a four-year term with an $18,000 annual salary; Dale and Lewis three-year terms at $15,000 a year; Wiggins and Cooper two-year terms ast $15,000 a year.

The lottery board will preside over what will be an estimated $100 million business in the nation's capital. The board will have the broad powers to decide which of the many competing lottery equipment firms recieve the coveted multimillion dollar contracts to operate the city's games.

The board will also adopt the rules and regulations that will determine which local businesses will be licensed to sell lottery tickets here. Those rules could set off a scramble for lottery licenses among small businesses that see lottery ticket sales as a potential revenue gold mine. In Maryland, store owners who sells lottery tickets receive a 5 percent commission on each ticket sold. Lottery ticket sales also increase traffic in many small businesses.

The lottery board will regulate dozens of bingo games and fund-raisers that now operates relatively free from any sort of controls and provide income for many churches and social clubs.

But first the board members, after their confirmation, will begin a search for a full-time executive director who will be paid $50,000 a year -- the equivalent of a Gs 16 employe. He will recommend rules and regulations to the board and oversee the opening of gambling operations.