Richard J. Davis, Virginia's Democratic candidate for lieutenant governor, said tonight in an interview that he believed his opponent, state Sen. Nathan H. Miller, violated state lobbying law in drafting and voting for legislation giving his legal clients $13.2 million in tax breaks and business advantages.

But in a public debate with Republican Miller later in the evening, the former Portsmouth mayor appeared to step back from his earlier statement, saying that he did not wish to judge his opponent and that he would "let the voters decide."

Davis' pre-debate remarks on what Miller has acknowledged as "an apparent conflict of interest" amounted to his toughest statement yet on the issue that has been dogging the Miller campaign for more than a month. Newspapers around the state have been almost unanimously critical of Miller's dual roles as state senator and utility lawyer, which were disclosed in a story in The Washington Post.

"It was certainly improper," Davis said in an interview before the start of the debate, which was sponsored by the Richmond Jaycees. "Any time a person has a private, immediate interest in something, it's almost impossible for him to be able to divide that personal preference from the objective view a legislator should have."

Miller, a 38-year-old attorney from the Shenandoah Valley, has acknowledged receiving at least $250,000 in legal fees from the state's electrical cooperatives while drafting and lobbying for their legislation. But he insists he has violated no law.

Questioned in last night's debate about the conflict-of-interest issue, Miller stuck to that strategy. "I intend to follow the disciplinary rules of the Senate of Virginia as I have for the past 10 years I've been here," he said.

Davis, 60, who like Miller is an attorney, later rejected suggestions that he was avoiding a direct confrontation with Miller on the matter. "I'm not soft pedaling it," he said. "I can give my opinion on it, but I don't want to go around being a judge of people."

A statewide poll released this week by two television stations showed Miller lagging five points behind Davis, while a poll conducted by the stations two weeks earlier showed the two candidates to be virtually even. In both polls, more than 40 percent of the voters listed themselves as undecided.

Meeting in their first public face-off of the campaign, Miller and Davis spent almost an hour swapping quips and digs over their plans for the state's No. 2 executive job. Largely a ceremonial office, the lieutenant governor's post in Virginia has traditionally been seen as a potential springboard for gubernatorial aspirants.

Throughout the debate, Miller hammered away at the issues that have become obligatory for conservative candidates in Virginia: the Equal Rights Amendment, collective bargaining for public employes and tighter gun registration laws. (He opposes all three.)

Miller also attempted to tie his campaign closely to the political fortunes of President Reagan and made repeated references to Davis' wealth.

Davis leaned hard on his background as Portsmouth's mayor and said he planned to improve communication between the state and local governments if elected. He referred several times to his service as a Marine during the Korean conflict. Miller has come into some criticism for filing as a conscientious objector in the early 1960s.

Davis, whose wealth comes chiefly from a Tidewater mortgage company he founded, also charged that Miller had been "not entirely accurate" in campaign claims that Davis wanted to "solve all our problems with more taxes." Davis said that he had only declined to rule out the possibility of tax increases.

Miller has said he would oppose all increases in taxation.