A House-Senate conference committee restored funding for the District of Columbia's new gambling board yesterday, clearing the last major obstacle to the start next April of a city-run, instant payoff lottery.

The conferees also completed action on the city's $1.9-billion budget for the year that began Oct. 1 by agreeing to a host of other provisions requested by city officials, including a record $336-million federal payment and a 16 percent pay raise for City Administrator Elijah B. Rogers.

D.C Mayor Marion Barry, who sat quietly as a spectator through most of the committee's deliberation, later described the final budget as a significant victory for the city. "This is history-making," the mayor said. "This is closer to what we requested than any other District budget in history."

The city lottery, which had been overwhelmingly approved by city voters in a referendum last November, had been jeopardized earlier this year when the House District appropriations subcommittee knocked out $628,000 in funding for the city's new Lottery and Charitable Games Board after subcommittee members complained that legalized gambling would be offensive in the nation's capital.

While restoring those funds yesterday, the conference also attached a string of restrictions, including one requiring that local rather than federal funds be used on lottery operations. In addition, lottery outlets were banned in Georgetown and such federal areas as the Mall, Rock Creek Park and along Pennsylvania Avenue NW between the White House and the Capitol. Lottery advertising will be prohibited on the Metro subway and Metrobuses.

Lottery board chairman Brant Coopersmith said later that the lottery games, which eventually are expected to bring about $25 million in annual revenue into city coffers, should begin during the next year.

The first game, he said, will involve instant "rub-off" lottery tickets that will be sold at hundreds of liquor stores, grocery stores, dry cleaners and other outlets in about five or six months. Players will be able to buy $1 colored tickets that, when rubbed, will reveal instantly whether they have won prizes ranging from $2 to $25,000.

By next fall, Coopersmith said, the city will also start a daily numbers game in which players will select a three-digit number ranging from 000 to 999 on automated terminals. The tickets will cost 50 cents and pay $250 to players who correctly select that day's winning number. The D.C. payoff will be the same as on the daily game in Maryland, but less than the typical $300 payoffs in the illegal games that have long been played on Washington's streets.

The five-member gambling board, which was appointed by Barry last July, must still approve final regulations governing the lottery, hire its staff and let contracts to private gambling firms that will operate the games for the city. But Coopersmith, who along with Barry and other city officials had lobbied vigorously to save the lottery from congressional extinction, said he foresees no further obstacles to the lottery's introduction if, as expected, the budget bill clears final passage in the House and Senate and is signed by President Reagan.

"We should be in business by next spring," he said. "We're really taking a great deal of pleasure from this."

The conference committee's action was denounced, however, by the Rev. John D. Bussey, a leader in the campaign against the gambling referendum last November. "This is a terrible travesty on the people of the District of Columbia," Bussey said. "It's the people who can afford this least who are going to be paying for it. If you look at other cities, all the gambling stations are in the black communities."

Bussey said it was especially ironic that lottery outlets were banned in Georgetown because "it's the people in Georgetown who can definitely afford it the most." The restoration of the $628,000 for the lottery board was accepted by House conferees yesterday at the strong urging of Sen. Alfonse D'Amato (R-N.Y.), the D.C. subcommittee chairman. He emphasized that he was "not endorsing lotteries as a revenue-raising measure," but defending the District's right under home rule to engage in an activity that had been endorsed by 64 percent of the city's electorate.

Coopersmith said that most of the restrictions imposed by the conferees would probably have been adopted by the commission anyway. The House members who had been the most vocal opponents of the lottery, most of whom represent states that have long had legalized gambling, said the amendments addressed their concerns about protecting the federal city from "degrading" and "offensive" lottery signs.

"This answers my principal objection that we not degrade the appearance of the capital with gambling and lotteries," said Rep. Lawrence Coughlin (R-Penn.), who introduced the amendment prohibiting advertising on Metro. "I felt it was important that we maintain the dignity of the federal enclave."

The gambling victory was only one in a series of major victories for the city during 90 minutes of back-and-forth haggling between D'Amato and seven House members, led by the D.C. subcomittee chairman, Rep. Julian Dixon (D-Calif.). D'Amato, a conservative who has recently emerged as a vocal defender of the city's interests on Capitol Hill, repeatedly urged his House counterparts to accept amendments inserted into the Senate version that were more favorable to the city.

On the federal payment, which is provided each year to reimburse the city for tax-exempt federal properties and the additional municpal service costs associated with being the nation's capital, D'Amato successfully fought a move by Coughlin to slash the $336-million level proposed by the Senate by several million dollars as a "symbolic" economy move. The House had approved a $300-million federal payment.

D'Amato and Dixon also fought for the amendment that will allow Barry to raise the pay of City Administrator Rogers from his current $52,800 to $61,400. Referring to reports that Rogers had received higher paying job offers from other cities, D'Amato commented that "it would be a tragic thing to lose such a capable administrator."

The conference committee also accepted a Senate amendment as a "one-time only" experiment allowing the city to submit its proposed budget to the Congress next year on April 15 rather than Feb. 1. City officials had said the extra three months will allow them to present Congress with more realistic revenue and expenditure estimates.