What if they gave an election and nobody came? That nearly happened last Tuesday when only 13,958 of the 259,000 registered voters in Northern Virginia's 10th Congressional District turned out for the three-way Democratic primary won by former Arlington state delegate Ira M. Lechner.

Election officials say the turnout, 5.3 percent of registered voters, was the lowest in a Northern Virginia congressional primary in the past decade. Although final figures are not yet available, the election cost taxpayers an estimated $38,000--or nearly $4 a vote.

"I've never seen anything that low, I was really surprised," said 10th District Democratic Chairman Mary Cahill of Reston. "Maybe the Senate conventions just overshadowed it."

In 1974, the last time the 10th District had a Democratic primary, more than 25,000 voters turned out to pick Joseph L. Fisher over three other candidates.

Exactly what this year's exceptionally low turnout presages for November, when Lechner will face freshman Rep. Frank R. Wolf, isn't clear.

On election night, moments after he learned he had gotten 84 percent of the vote and carried every precinct in the 10th District, an elated Lechner predicted "a resounding Democratic victory in November."

Others, including members of his own party, are less certain. They attribute Lechner's victory to superior name recognition, his 22-year involvement in Northern Virginia politics and the fact that he has run for lieutenant governor twice since 1977 and can call upon the services of a cadre of loyal and efficient party workers.

It also helped, party insiders say, that Lechner's opponents, Rose Z. Thorman and Edward D. McLaughlin Jr., were first-time candidates with little recent involvement in local politics.

"People didn't know there even was a primary," said Arlington County Sheriff Jim Gondles, a Lechner supporter and Democratic Party strategist. "This was the only primary in the state or the entire metropolitan area. And the ones who did know knew Ira was going to win, so there was no reason for them to go to the polls."

Republicans already are predicting that the primary turnout indicates the Democrats could be in trouble come November.

"Lechner's victory means he had the support of the Democratic establishment and the party activists," said House Minority Leader Vincent F. Callahan Jr. of Fairfax County. "As a Republican I was heartened by the very low turnout. The Democrats used to outvote us four or five to one around here, but two years ago we got 17,000 people out to vote in a Republican primary.

"I think the significant thing about the low turnout is that there didn't seem to be a mass of anti-Reagan sentiment out there or more people would have turned out. After all, they had three candidates to choose from."

Some officials question the value of spending roughly $38,000 to hire poll watchers to staff 166 precincts, custodians to service voting machines and printers to make sample ballots. That, of course, does not include the estimated $70,000 the three candidates combined spent printing campaign signs and brochures, on direct mail solicitations, on radio ads and headquarters space.

"Conventions have become more popular in recent years because of low voter turnout, candidates' expenses and party expense," said Joan S. Mahan, secretary of the Virginia State Board of Elections.

Cahill said the Democratic Committee of the 10th District, which includes Arlington, Loudoun and northern Fairfax counties, Falls Church and Fairfax City, has in recent years opted for a primary over a convention.

"A primary is more democratic," she said. "If there had been a convention, Rose and Ted would never have had a chance."

Lechner and Wolf are not the only candidates in the fall race. On the eve of the primary, Scott R. Bowden, 28, of Falls Church filed papers to become the candidate of the Libertarian Party.

Bowden, a program analyst for a suburban computer firm he declined to name, said he wants to "return to basic American values" and advocates "individual rights and much less government."

In 1980, in the neighboring 8th Congressional District, third-party candidate Deborah Frantz, who advocated legalization of marijuana, got enough votes to cost Democratic Rep. Herb Harris his seat.

"I expect to get 4 or 5 percent of the vote," Bowden said. "If I'm lucky I'll be the difference between who wins and who loses."

And he'll have done it without a primary.