District of Columbia voters yesterday overwhelmingly approved citizen initiatives that would legalize lottery and daily numbers games in the nation's capital and set the District on a possible path to statehood, while Democrats retained their virtual lock on city politics.

The gambling measure was winning by a nearly 2-to-1 margin with more than half of the vote counted. If it is not rejected by Congress or the City Council, the proposal could, by mid-1981, give the District a government-run gambling operation similar to the one in Maryland that many city residents now patronize.

The statehood initiative was being approved by a margin of nearly 3-to-2, and its supporters predicted last night that a constitutional convention to draw up a proposed D.C. state consitution could begin next July 4. However, even with the passage of the referendum, statehood is far from automatic, requiring congressional approval that in other instances has taken years or even decades.

The two measures were the first initiatives ever approved by District voters.

Despite Republican Ronald Reagan's sweeping presidential victory and Republican gains throughout the country, President Carter defeated the President-elect by a 5-to-1 margin in the District, with independent John B. Anderson trailing far behind D.C. Del. Walter E. Fauntroy, a Democrat, was easily reelected to a sixth term as the District's nonvoting delegate to the House of Representatives.

Democrats also won five of six City council seats being contested. Incumbent Democrat John L. Ray, a 37-year-old lawyer, was leading a seven-way race for one of two at-large seats, with incumbent Republican Jerry A. Moore Jr., a 62-year-old Baptist minister, winning the other Realtor H. R. Crawford, a 42-year-old Democrat, became the only new council member elected yesterday, winning over three opponents in Ward 7. Incumbent Democratic council members John A. Wilson (Ward 2), Charlene Drew Jarvis (Ward 4) and Wilhelmina J. Rolark (Ward 8) also handily won reelection.

Local victories were overshadowed for District Democrats, however by Reagan's convincing win. Fauntroy predicted that Reagan, who during his campaign opposed or took no position on most key D.C. home rule issues, will prove to be a major stumbling block to self-determination for the city.

"With the arrival of a Reagan presidency and fiscal conservatives elected on a tideof right-wing conservatism, we're going to have a more difficult time in receiving the formularized federal payment, (city) budget autonomy and the commuter tax," he said. "The whole self-determination thrust we had envisioned for the next four years . . . it's going to be difficult."

Mayor Marion barry, who had planned to go to a Carter victory party last night but decided not to attend after Carter's defeat became apparent, was reluctant to talk about the prospect of a Reagan presidency. "We'll see," he said. "Nationally, we're disappointed that Carter didn't win. We'll reach out to Gov. Reagan, advise him."

Barry refused to take a position before the election on the gambling measure, though he had supported legalized gambling in the past and was widely viewed as a closet supporter of the proposal. He promised to move quickly to implement the provisions of the initiative, which calls on him to appoint a gaming board to administer the city-run games. "The people have spoken and when the people speak I listen -- sort of like E. F. Hutton," the mayor said.

Supporters of legalized gambling in the District, who have predicted that the financially strapped city could reap up to $35 million annually in gaming revenue that now goes to Maryland, tried unsuccessfully to have a gambling referendum approved last May. Many blamed the defeat of the earlier measure on provisions which would have legalized pari-mutuel betting on dog racing and jai alai. This time around, however, the measure contained only the lottery and numbers games.

"What the people voted for was very diferent from what we had in May," said a jubilant Ron Cocome, chairman of the D.C. Committee on Legalized Gambling, the primary group supporting the gambling measure. "The people have already expressed thatthey did not want parimutuel betting. People either wanted the revenue or thought they were going to win the lottery."

As in the spring, a group of black clergy, most of them Baptists, attempted to block the gambling measure. But they had to run this campaign without the help of animal lovers who objected in May to what they called cruel training methods employed in dog racing, and without those who feared jai alai might attract organized crime, including U.S. Attorney Charles F. C. Ruff.

Despite their defeat, the ministers were philosophical last night about the prospective start of gambling in the District. "My feelings are simply that when you put it to the people and the people vote, that's it," said the Rev. John D. Bussey, one of the chief opponents of legalized gambling. t

However, another gambling opponent, C. H. Johnson, said the wagering foes may attempt to get Congress to veto the gambling bill before it can take effect.

The gambling measure was winning approval in all eight city wards, but the statehood initiative was only winning in seven. The exception was Ward 3, the affluent, mostly white area west of Rock Creek Park, where statehood was going down by a 5-to-3 margin.

"We figured we'd lose in Ward 3 and win everywhere else," said Ed Guinan, one of the chief supporters of the measure. "We didn't think that in the well established, affluent areas where people do very well, that people would be anxious to change the [existing limited home rule] structure."

The statehood measure was supported by virtually all the District's major political figures, though none actively campaigned for it. The lone exception was Fauntroy, who argued that the measure would prove too costly and would interfere with his own efforts to win ratification of the Voting Rights Amendment to the Constitution, now stalled.

"I feel this was really a kind of declaration of independence," Guinan said, "especially when there's a more conservative wave on the national level." In a reference to the Voting Rights Amendment, the main alternative to statehood as a way for the District's residents to gain voting representation in Congress, Guinan said, "People said they didn't want half a pie. "They said let's go for the whole pie."

The statehood measure spells out a complex process leading eventually to a vote by Congress on whether to admit the District as the nation's 51st state.First, the measure provides that voters must go to the polls again to choose delegates to a constitutional convention.Guinan said statehood backers would seek to hold that election next May, and shoot for July 4, 1981, as the opening date for the convention.

After the constitution is drafted, it must then be approved by voters. Then the mayor would submit the document to Congress, and a simple majority vote of both houses could make the District a state. The procedure parallels that taken by other states when they sought admission to the union. It is a long process, however, sometimes taking decades.

Despite yesterday's cool and rainy weather, the election attracted a sizeable turnout in the District.

Wilson raised more than $80,000 for his campaign. But even in winning 78 percent of the vote in Ward 2 his vote percentage was smaller than that recorded by incumbents Jarvis and Rolark, neither of whom has served on the council as long as Wilson has. Jarvis was collecting 93 percent in Ward 4, and Rolark 92 percent in Ward 8. Crawford won with about 84 percent of the vote in Ward 7.

The D.C. Statehood Party retained its status as an official party, with Josephine Butler, the party's candidate for Fauntroy's seat, receiving well more than the required number of votes.