The three Republicans who want to run against Democratic Rep. Herbert E. Harris II in Northern Virginia's 8th District warmed up for the June 13th primary with a midnight lottery.

At a prearranged meeting Thursday night, the three challengers - John F. Herrity, chairman of the Fairfax County Board of Supervisors; and State Dels. Robert E. Harris and Robert L. Thoburn, both representing southern Fairfax - drew lots from a wooden bowl at the home of district party chairman Barbara Hildenbrand to see who would get top billing on the primary ballot.

Haris, who is sometimes confused with Democrat Harris, won the lottery. Thoburn will be listed second, and Herrity, who many observers think is the most formidable candidate, will be third.

Although the filing deadline is two weeks away, no other candidates - at least not major ones - are expected to run for the Republican nomination.

Republicans liked to consider the 8th District their territory, but in 1974 - two years after the areas and exclude rural areas - Democrats took control, under Herbert Harris. The 8th includes southern Fairfax, Alexandria, Prince William Country, Manassas and northern Stafford County.

Herrity in 1975 won a surprisingly decisive victory over Democratic incumbent Jean R. Packard for the chairmanship of the Fairfax Board of Supervisors. He has hired as his campaign manager a former Republican National Committee staff member who played a key role in the recent upset of Democrat Bella Abzug by Republican William Green in the special election for the New York congressional seat that had been held by Mayor Edward Koch.

The campaign manager is Donald K. Allen, who was in charge of the phone bank that contacted "disgruntled" Democrats in the district.

While serving as chairman of the Fairfax board, Herrity has maintained a high profile on a number of headline-grabbing local and regional issues.

He led the way on the board's decision to endorse extension of I-66 from the Capital Beltway to the Potomac River and removal of a sewer moratorium that was holding up industrial development in the area around Dulles International Airport.

He was one of the early advocates of a reappraisal of Metro as a full, 100-mile system, but has been frequently rebuffed by his board when he sought to halt county subsidy payments for Metro rail and bus deficits.

Late last year, when it became apparent Herrity would run for Congress, other board members - Democrats and Republicans alike - showed increasing resistance to his leadership, and sometimes left him as a minority of one.

Herrity, who runs an insurance business out of his Springfield home (he is also a lawyer), suffered manship. But his doctor said recently he is healthier than the vast majority of people.

Robert Harris promised to wage a tough campaign against Herrity, but after initially dwelling on Herrity's heart-attack history, he said he considered the issue closed.

Harris has said said repeatedly high taxes were the No. 1 concern of residents in the 8th, and he maintains he has kept faith with them in his votes in the General Assembly.

He opposed both the Northern Virgina gasoline tax increase in 1976 (though enacted in Richmond, it was never implemented because of Fairfax City's opposition) and the sales tax increase that failed by one vote in the House of Delegates during the recently concluded 1978 session.

Those votes angered Harris's Northern Virginia colleagues - Republicans and Democrats alike. In 1976, he was criticized by other legislators for his absences and again in 1977, the year he broke his leg.

Harris ran unsuccessfully for Congress as an independent in 1972.