By the city assessor's reckoning, Eunice L. Carpenter has a lawn worth $10,142 alongside a modest Northeast Washington home valued at $35,000.

It seemed like too much when the assessment notice arrived in the mail several weeks ago, so Carpenter applied to have the valuation cut. Yesterday, taking advantage of some free time while on jury duty, she went to the District Building to plead her case.

Like hundreds who will follow the same process in the next several weeks, Carpenter appeared before a hearing panel of an obscure District of Columbia agency called the Board of Equilization and Review.

The board's sole job is to review assessments prepared by the city's Department of Finance and Revenue-to determine whether they are too high, or too low, or are out of line with the pattern of values elsewhere in a neighborhood.If it finds the assessor was wrong, it can adjust the valuations, reducing or raising a tax bill.

For Carpenter, a retired budget analyst for the Army, yesterday's appearance began with a friendly greeting from Joseph Dixon, the panel chairman. She was invited to represent her case.

It went back to 1949, she said, when she and her late husband bought a 25-foot-wide lot next door to their home at 4942 Blaine St. NW for $700. Legally too narrow to build on, the Carpenters turned it into a lawn.

Last year, it was assessed for $3,336, representing an estimate of its real cash value. This year, when the notice arrived, Carpenter was startled to find that the valuation had jumped to $10,142-a rise of 204 percent.

The valuation of the adjacent Carpenter home-a modest semidetached structure-and the lot on which it stands was increased by 24.7 percent, to $35,000. That meant all the Carpenter property was valued for tax purposes at $45,142.

The increase in the value of Carpenter's vacant side lot follows a pattern that emerged this year in the city, with assessors putting relatively higher valuation on vacant land than on structures.

Donald R. Beach, the chief assessor, has said the really significant figure is the total value of an individual homeowner's property, not the value of part of the holding, such as Carpenter's side lot.

After the panel heard Carpenter's story, chairman Dixon scanned the assessor had groofed, thinking the lot was a suitable building site that could be sold.

Dixon said Carpenter would get a reduction, but he would not say how much. She will receive a letter soon informing her of the new figure.

Appeals to the board have risen sharply in recent years, keeping pace with the rise in assessments in the city, according to Samuel C. Reynolds, the full board's part-time chairman.

Reynolds said there were 752 appeals in the 1977 tax year, 1,352 in 1978, and 1,794 a year ago, when 1979 tax bills were being prepared. Since the deadline for filling appeals for the 1980 tax year was Monday, Reynolds said the total work load will not be known for several days. Individual taxpayers will be notified when to appear.

When the hearing schedule reaches its peak, four panels composed of real estate experts and appraisers will hear appeals simultaneously in the same room.

Of the 1,749 taxpayers who filed appeals a year ago, Reynolds said, 646 received reduced valuations totalling $69.4 million, while five owners of large properties got increases totalling $1 million. In most of the remaining cases, the panels decided the assessort had valued the properties for what their owners could have sold them. CAPTION: Picture 1, Phoebe C. Trice opens backlog of assessments mail. Photos by Douglas Chevalier-The Washington Post; Picture 2, Eunice Carpenter, left, explains why she feels her property has been assessed at too high a rate to Board of Equalization and Review members, from left, Marion H. Jackson and Joseph T. Dixon.