One byproduct of the protracted fight over the D.C. Lottery Board is an effort by some city officials to take a second look at provisions of the voter-approved initiative that set up legal gambling in the city.

Council member Nadine P. Winter (D-Ward 6) is working over legislation that would change the makeup of the board and bring it more directly under city control. Others on the council are pursuing ideas of their own. While they're at it, officials might be well advised to consider the law's relatively weak provisions limiting involvement in the legal lottery by persons with past or present criminal associations.

A top official of the firm that holds the city's instant-winner lottery contract was convicted in 1972 of operating an illegal lottery. A principal owner of another firm that recently was awarded the city's daily numbers contract was arrested in 1973 on a charge of operating an illegal lottery, but that charge was dismissed. Both men have fathers who were convicted of involvement in illegal numbers games.

A comparison between the District's regulations and those of other jurisdictions is difficult because the D.C. government is unique in allowing private firms to run its lottery operations. Other governments run their own operations.

However, the city's restrictions fall far short of requirements in New Jersey and Nevada--two states that do license private businesses to run casinos.

In the District, the gambling law doesn't spell out disqualifying conduct of potential bidders on city lottery contracts but merely prohibits anyone who has been convicted of a felony within five years from selling or supplying bingo equipment, according to Jeanette Michael, counsel to the lottery board.

The lottery board, whose discretion under the law was unclear, adopted that five-year limitation for all private persons wanting to do business with the board, officials said.

In New Jersey, the standard for casino operators is 10 years without a felony, according to Tony Parrillo, deputy director of the state's division of gaming. "Even after 10 years it's still evidence and the person has a tough burden to prove he is rehabilitated," Parrillo said.

Equally important, Parrillo said, is a provision that state officials also may take into account an individual's "association with career offenders" and source of financial backing.

A state gaming official in Nevada said the state's three-member gaming control board can consider anything "that can cast a shadow on the state of Nevada." The official said the casino operations "are a license, not a right."

District lottery officials have defended the city's weaker law, arguing that stricter regulations might prove to be unfair to blacks, who they said have been the victims of racial discrimination and questionable police tactics that resulted in police records.

What confronts the city now, others suggest, is the need to find a way to balance the concern about racial discrimination and its ugly effects while at the same time assuring the integrity of the city's lottery.

The District, with a paltry three electoral votes, hasn't exactly been a hotbed of 1984 presidential campaign activity up until now, but things are warming up a bit.

Mayor Marion Barry has met several times with black leaders from across the country to consider ways of influencing the outcome of the election, including fielding a black candidate. Barry also has heard out former vice president Walter F. Mondale and several other major Democratic contenders, who are seeking the mayor's support.

Attorney Robert Washington Jr., a prominent supporter of Barry's, said he recently was named cochairman of Colorado Sen. Gary Hart's D.C. presidential campaign committee. Robert Miller, a legislative assistant to City Council member Polly Shackleton (D-Ward 3), resigned to join Mondale's national campaign staff as a researcher and speech writer.

Finally, Sen. Alan Cranston (D-Calif.) edged Mondale in a survey of members of the Gertrude Stein Club, the area's largest gay organization, that was conducted during the recent Gay Pride Day.

Cranston, whose liberal voting record has attracted gay support nationally, was favored by 35 percent of the 1,520 Stein members surveyed who live in the District, compared to 24 percent for Mondale.

Among the other Democratic candidates, Hart received 15 percent and Sen. John Glenn (D-Ohio) received 10 percent.