Lynne and Larry Pilot were shocked by the letter from the county courthouse.

The bad news: Their three-bedroom brick home in Lyon Village, near the Clarendon Metro stop in Arlington County, is now worth $161,800 -- more than 20 percent above last year's property tax assessment.

When the Pilots, both lawyers, brought their home 11 years ago, they paid $40,000, assumed a 5 1/2 percent mortgage and paid about $500 in property taxes. "We thought it was a vast amount of money at the time," Larry Pilot says wistfully.

If the county's projected tax rate holds, the Pilots will pay $1,975.40 in property taxes this year.

Residents and almost all county officials agree on the cause of the escalating tax burden.

"I can sum it up in one word -- Metro," said Anton S. Gardner, the county's chief of fiscal affairs as he placed his finger on the Clarendon stop on a wall map in his office.

The Orange Line is the first spur on the subway to reach into what real estate agents like to call the "highly desirable" Virginia Suburbs. Housing prices have shot up, along with assessements.

Although the increase in the Pilots' property tax is above the county average of 18 percent, it is well below increases reported by some of their Lyon Village neighbors. They are complaining of 33 percent rises this year and almost 50 percent over the last two years.

The Lyon Village area increased an average of 20.2 percent this year. In neighborhoods around the Ballston stop, where the Orange Line now terminates, assessments are up an average of 24.4 percent, although assessors say that the percentage is skewed by commercial rezoning.

While county officials admit they have been fielding calls from many irritated taxpayers, they say they are confident that the assessments are fair and reflect the true value of property in Arlington neighborhoods.

"The market is going to absorb those prices easily," said Gardner. "In Lyon Village, you could put anything out there and it would sell."

Some residents, however, say they are not interested in selling and that all they see in their future is enormous tax bills.

"Lyon Village is suburban living on a subway line and lots of people want to buy here because of it," said Ray Anderson, who last year absorbed the tax-time frustrations of his neighbors as president of the Lyon Village Citizens' Association. "But everybody here right now is stuck."

"We couldn't afford to move if we wanted to," said Lynne Pilot. "Where would we ever find mortgage money like that again?"

Only 17 homes of the 500 in the village changed hands last year, according to County Tax Assessor James R. Vinson.

While the assessments should be directly related to what the houses will fetch, many residents say houses up for sale now languish on the market because of the high prices and interest rates.

"These are very tough times and it's not so certain houses will sell at the prices they are appraised at," said Larry Pilot.

County Board Chairman Walter L. Frankland Jr. conceded yesterday that residents like those in Lyon Village are in "an unfortunate position" and said that board members would "try to wipe out the effects of assessment."

"The pressure point is on the County Board to bring the tax rate down to a reasonable level," Frankland said.

The board, facing a May 1 deadline for its 1981 budget, has advertised a tax rate of $1.21 per $100 assessed valuation, down from $1.29 last year. Once the rate has been advertised, the county cannot raise it, but can lower it if it wishes.

Frankland and other members of the board's Republican-backed majority have said they hope to find a way to push the tax rate as low as $1.19, perhaps by trimming proposed pay increases for county employes.

Meanwhile most Lyon Village residents seem resigned to paying their ballooning tax bills.

"We're going to approach this in the most reasonable way," said one homeowner. "Just don't expect any parades at the courthouse."