The private firm that has been removed from advertising the District's current instant lottery game is demanding about $200,000 in additional payments from the lottery board for expenditures the company says it made in promoting previous games, city lottery officials said yesterday.

Chester C. Carter, the lottery board's executive director, earlier this week ordered LaMancha Inc., the advertising firm, to halt any further advertising for the instant game that began yesterday. Carter's action was part of a major policy change in which the board has decided to take direct control over the advertising for the instant lottery games.

Carter told the lottery board yesterday that payment of the additional funds has been made a condition of negotiations aimed at formally modifying the the board's contract for the instant games.

The board, meeting as the committee of the whole, did not adopt a modification to the contract and took no action on LaMancha's request except to direct Carter to continue to try to negotiate a settlement.

In other business yesterday:

* Board Chairman Brant Coopersmith complained that installation of computer terminals for the daily numbers game is behind schedule because the Chesapeake & Potomac Telephone Co. is not hooking them up quickly enough. Coopersmith said that C&P's slowness is causing the city to lose hundreds of thousands of dollars in lottery revenues. The board had hoped to have terminals installed in 300 sales locations by Oct. 15, but only 176 are operating.

* Carter said that he plans to conduct preliminary discussions with Maryland lottery officials about the possibility of a joint pool of prize money for Lotto, a new numbers game the board is planning to launch this spring. Carter said that a joint pool would allow both jurisdictions to offer larger prizes.

Most of the discussion at yesterday's meeting centered around the advertising issue. Board members Carolyn B. Lewis and Almore Dale complained that LaMancha had failed to provide the board with sufficent documentation to show how it had spent about $2.5 million in lottery revenues it received to advertise the four previous instant games over the last year.

LaMancha did the advertising as a subcontractor for a joint venture led by Games Production Inc. (GPI), a private firm hired by the board to run various aspects of the instant game, including the advertising.

Gloria Decker, GPI's general manager, told the board that LaMancha has provided the board with detailed advertising budgets for each of the instant games as well as receiving approval for each game's advertising campaign.

Decker said in an interview that LaMancha has not submitted to the board additional documentation showing how the money has actually been spent because it has turned over that information to the city inspector general's office, which has been auditing LaMancha's expenditures.

Decker said LaMancha decided to await completion of the inspector general's report before submitting the information to the board.