The District of Columbia appears headed for decisive and far-reaching changes if voters approve, as expected, two proposals on the ballot in Tuesday's election. One of these would legalize a lottery and daily numbers game in the nation's capital, while a second would authorize a constitutional convention to set the District on a possible path to statehood. c

The enthusiasm over the two local issues, though often limited, nevertheless has overshadowed the presidential election in this overwhelmingly Democratic town. President Carter, who won decisively here in 1976 with 82 percent of the vote, is expected to capture the District's three electoral votes easily again this year.

Del. Walter E. Fauntroy, with only nominal opposition, can count on retaining the job he has held since 1971. And five incumbent council members likely will be reelected with overwhelming majorities, meaning that next year's council will look almost identical to its present appearance.

The one newcomer to the city's legislature likely will be H. R. Crawford, the Ward 7 Democratic primary winner, who is considered a virtual shoo-in for the council's only vacant seat.

The two referenda have dominated most of the political discussion this election year and have attracted the most money, the most interest and most lively campaigns.

The debate on each of the initiatives has evolved against the backdrop of the city's worsening budget crisis and each has in some way been touted as a possible solution to that problem.

Proponents of the measure to legalize the city-run lottery and daily numbers games contend that legal gambling is a short-term solution to the city's current cash shortage and a revenue source that could add at least $35 million a year to the District government coffers immediately.

The proponents of statehood -- and they include most of the city's elected leadership -- contend that the District's financial problems stem from the city's dependence on the federal government, the local government's lack of budget autonomy, and its inability to levy such measures as a commuter tax. Supporters of the initiative say that statehood is the only way the District can achieve full home rule and control over its own fiscal affairs.

Both initiatives have attracted opponents, but they are few, and apparently without the groundswell of support needed to defeat the referenda at the polls. w

For voters who think there is no choice for president this year are eight presidential candidates whose names will appear on the District ballot. Besides Carter, Republican nominee Ronald Reagan, and Independent John B. Anderson, voters can select from Citizens Party candidate Barry Commoner, Libertarian Ed Clark, Deidre Griswold of the Workers World Party, Communist Gus Hall and Socialist Workers Party candidate Clifton DeBerry, a stand-in for party nominee Andrew Pulley who is too young to be put on the ballot.

Carter's 82-percent landslide against Gerald Ford in 1976 should be trimmed back slightly this year, because of a vigorous Reagan campaign for black votes and some Anderson support among liberal Republicans and former supporters of Sen. Edward Kennedy (D-Mass.) in Ward 3, West of Rock Creek Park.

Fauntroy, with no real opposition, appears headed for a comfortable victory primarily because many District political figures see the delegate's post as being too far removed from the power that comes with actually running the city.

Fauntroy is challenged by 31-year-old Republican Robert Roehr, a salesman and member of the Gay Activists' Alliance who is considered a maverick liberal by the city's Republican structure and did not receive the party's official endorsement. The GOP's backing went to write-in candidate Bill Keyes. Also running is D.C. Statehood Party candidate Josephine D. Butler, who has used her campaign as an opportunity to publize the statehood initiative.

Democratic City Council member John L. Ray, a 37-year-old attorney with acknowledged ambitions for higher office, is expected to lead a field of seven candidates for two at-large Council seats. Ray won a convincing victory against scant opposition in the Sept. 9 primary election. Incumbent Republican Jerry A. Moore, 62, is favored to retain his seat by finishing second, but has been harshly attacked by independent candidate Joel Garner, a 33-year-old researcher with the U.S. Department of Justice.

Also competing for an at-large seat, but given less of a chance to win, is D.C. Statehood Party candidate Charles Cassell, a 56-year-old architect. Glenn B. White, a 26-year-old Metro track laborer, is the at-large candidate of the Socialist Workers Party. Two others are running as independents: Maurice Jackson, 20-year-old District and Virginia director of the Communist Party USA; and Charlotte R. Holmes, a 53-year-old budget analyst for the Small Business Administration.

Crawford, 42, beat two opponents in the September Democratic primary in Ward 7, which occupies the far eastern corner of the city, and is favored on Tuesday. Running against Crawford are Republican John West, a 47-year-old contractor; and two independents, 39-year-old business consultant Durand A. Ford and chemist Maryland D. Kemp.

In Ward 2, stretching from Foggy Bottom through downtown to Shaw, incumbent Democrat John A. Wilson, 36, has received a spirited challenge from Republican Ann Kelsey Marshall, a 29-year-old free-lance writer. Wilson raised more than $80,000 for the contest and is favored.

Charlene Drew Jarvis, the incumbent Democrat from Ward 4 in upper Northwest, is favored over 56-year-old business consultant and retired city government worker Israel Lopez, the Republican candidate.

And in Ward 8, the city's poorest ward stretching through Far Southeast, incumbent Democrat Wilhelmina J. Rolark, 63, is expected to win over two opponents -- Republican Leon F. Parks and independent Kellis Sylvester. A fourth candidate, Leona Redmond, withdrew from the race.