Virginia Lt. Gov. Richard J. Davis today won the Democratic party nomination for the U.S. Senate, sweeping to a second-ballot victory that buoyed party hopes of recapturing Sen. Harry F. Byrd Jr.'s seat in either a two- or three-way race.

Davis, a 60-year-old millionaire mortgage banker from Portsmouth with a moderate-to-liberal image, moved quickly to make President Reagan's economic policies the central theme of a campaign that could find him running against two conservatives, Rep. Paul S. Trible Jr., the Republican party nominee, and Byrd, the Senate's only independent. Byrd, who had announced he would retire from Congress in January after 18 years, is expected to announce Tuesday whether he will change his mind and seek reelection.

"It is unsatisfactory to me that we have the highest unemployment rates since the Depression, the highest interest rates internationally since the time of Christ and highest rate of business bankruptcies," said Davis at a brief post-convention news conference.

Davis' triumph followed an emotional two-day convention which saw other declared candidates--including former Rep. Joseph L. Fisher of Arlington and prosecutor Robert F. Horan of Fairfax County--refuse to bow out despite obvious signs that the lieutenant governor had the nomination sewed up. Many Fisher and Horan supporters were furious last night when Davis, after having taken himself out of the running two weeks ago, announced that he would accept the nomination.

Today, a defiant Fisher, who jumped into the race under the expectation that Davis was out of it, told cheering supporters, "I'm in this thing to the end. I'm going to do it, do it, do it."

The Fisher charge briefly elated his backers, but the boomlet for the 68-year-old former congressman quickly fizzled. On the first ballot, Davis won 1,369 votes--175 short of the majority needed for nomination, compared to 704 for Fisher, 166 for Horan, 405 for state Sen. Virgil Goode of Rocky Mount, with the rest scattered among an assortment of favorite sons, including Senate Majority leader Hunter B. Andrews of Hampton, state Del. Owen B. Pickett of Virginia Beach and former state Attorney General Andrew P. Miller of Alexandria. More than half of Fisher's support came from northern Virginia.

On the second ballot, however, the favorite son votes shifted in droves to Davis and Fisher quickly took the podium to make the traditional motion that the nomination be made unanimous. Horan had released his delegates immediately after the first ballot.

Nonetheless, the events left a bitter taste in the mouths of some Fisher supporters still angry over the nominee's earlier indecision. "It put an unnecessary stress and strain and hassle on the party," said Sen. Clive L. DuVal of Fairfax. "I wish he would have just made a decision and stuck to it."

Davis was believed by many to be the party's strongest candidate because of his business background, reassuring to conservatives, and his record of support for some causes such as the Equal Rights Amendment.

True to Virginia tradition, Davis today gently tread on the legislative record of Byrd, whose recent hints that he may reverse his earlier decision to retire has dramatically altered the calculations for the fall campaign. Asked about Byrd at his post-convention news conference, Davis said "there may be some differences in our philosophies" on such issues as aid to the cities. But Davis said he is in accord with the senator's stand for a strong national defense and "fiscal responsibility." He also said he has "no preference" as to whether the three-term senator runs again.

Other Democrats, however, were elated at the prospect that Davis could seize the middle ground in a three-way race, leaving Trible and Byrd to divide up the state's conservative vote. Former Virginia Lt. Gov. Henry E. Howell of Norfolk brought down the convention earlier by saying: "I want you to know that at 2:30 this afternoon I have to leave for the parking lot to circulate petitions for Senator Byrd to run again."

As mayor of Portsmouth during the mid-1970's, Davis forged a coalition of labor unions, blacks and businessmen to revive the ailing port city. He was elected chairman of the state Democratic party after a 1977 Republican sweep had plunged the party to its lowest point in years, and was widely credited with rebuilding the party's sagging machinery.

Davis, a Catholic who rose to wealth from humble origins, was one of three Democratic statewide candidates who swept their party to victory in last November's elections. He still has three years left to run in his term as the state's second highest executive, and said he will not step down from the part time position during the campaign.

Davis' nomination capped a series of extraordinary convulsions within the Virginia Democratic Party which, some say, may be be pivotal in shaping the party's future.

Frozen out of statewide office for 12 years, the Democrats came away from their victories last fall determined to maintain harmony among their disparate factions. To that end, party leaders met privately last winter to produce a senatorial candidate who could ride into the office with the same coalition that elected Robb.

But those hopes were short-lived. Within a month of selecting Pickett as the Democrat with the "least negatives," the party leadership--Robb included--was buffeted from all sides.

There was, at first, grumbling among party regulars about the closed-door process that produced Pickett, reminiscent to many of the backroom, machine politics of the old Byrd organization. The grumbling was heightened by Pickett's obvious failure to excite party regulars. A little-known lawyer and accountant from Virginia Beach, he was plagued from the outset by an inability to raise money and a lackluster speaking style that disappointed the party faithful.

Meanwhile, there were other presssures building within the party's tenuous coalition. Blacks--who overwhelmingly supported Robb and comprise almost one-fifth the state's population--were incensed when Pickett launched his campaign by invoking the Byrd's name. The senator's diehard stand for segregation as a state legislator in the 1950's is still vividly remembered by many blacks. Also, state Sen. L. Douglas Wilder of Richmond, Virginia's most influential black legislator, angered by the state legislature's off-handed rejection of several black issues, went to the brink with an independent Senate campaign. He withdrew only after extracting the price of Pickett's exit.

That price was, in turn, unacceptable to some conservatives who had backed Robb's campaign. Some of them--members of the old Byrd guard --struck back first by withholding financial support from several potential Democrat candidates and finally, by trying to propel Byrd himself back into the race.