Kim Lisa Sobotta's school lunch last Friday was fried chicken, a mound of whipped potatoes with gravy, one buttered roll, lime jello with fruit and milk.

Cost to prepare: 84 cents. Selling price in her Arlington school: 60 cents.

In the District of Columbia the same day, Tameka Corley's lunch tray carried oven-fried fish fillet on a bun, tossed salad of lettuce and tomato, buttered peas and corn, half a chilled pear, milk and cake.

Cost to prepare: $1.54. Selling price: 35 cents.

Over the course of a school year, students in the two school systems -- and others around the Washington area, for that matter -- will be given lunches with about the same overall quality and nutritional value. Both school systems also receive basically the same federal subsidy, 33.5 cents for each full-priced meal, to help meet the costs of preparing lunches.

Despite the similarities of what goes on the tray, the programs behind those lunches are almost a political and social statement by the school systems.

Arlington school officials resolved almost a decade ago to eliminate lunch deficits that reached $437,000 in 1971. They devised a more efficient system involving a labor-saving central kitchen and raised prices to among the highest in the area. Last year, the school system made a $36,000 profit on its lunch program, enabling it to put the money in the bank and avoid diverting funds intended for textbooks or other educational purposes, to food preparation expenses.

In the District, the social and economic problems were larger and more complex. The D.C. school system, which serves 58,600 students to Arlington's 6,500 had a $5.1 million deficit in the school lunch program last year.

The deficit comes at a time when the District government is beset by huge budgetary problems and is under heavy pressure from Congress to find ways to cut costs.

The District's losses last year were due to higher preparation costs for meals and significantly lower student prices because of the larger number of poor children in the city.

In addition, the District must rely on commerical lunches for those schools that do not have cooking facilities. About one-third of the lunches served each day in District school cafeterias are purchased under a contract arrangement from Morton's Foods, an ITT subsidiary that specializes in mass-producing TV dinners and the like.The lunches are delivered to the schools, where they are heated and served.

Seven school jurisdictions in the Wasington area provide 265,000 hot lunches each day to youngsters from kindergarten to high school. Preparation costs and prices range widely, generally reflecting economic concerns and managerial tecniques in the varying jurisdictions.

Prices range, for example, from a low of 35 cents in District elementary schools to a high of 70 cents in Falls Church secondary schools. Free meals and lunches at reduced prices are available to thousands of eligible students in all the school systems.

The lunch programs try to be self-supporting, so that their expenses don't exceed the money taken in from students and from government cash and commodity subsidies.

Alexandria, as well as the District of Columbia, failed on that score. The Alexandria school board had to appropriate $90,000 last year to supplement its lunch program. But Fairfax County, Falls Church, and Montgomery and Prince George's counties managed to stay profitable, along with Arlington.

Here is what other school systems spend to prepare an average lunch: Prince George's County, $1.13; Fairfax, $1.20; Alexandria, $1.24; Montgomery County, $1.31.

Tiny Falls Church, which serves only about 560 lunches each day at its three schools, spends $1.54 to prepare a meal.

Peggy McConnell, director of the Fairfax program, which serves 73,000 lunches, had the most complete profile of how costs are divided. She said the $1.20 her system spends on an average lunch includes 60.88 cents for food, 37.22 cents for labor, 10.89 cents for supplies and 11.58 cents for indirect costs.

Differences in the lunch programs are sure to become more visible in the fight now shaping up over President Carter's proposal to reduce the federal subsidy by 5 cents for each meal served to middle-and upper-income students.

Cafeteria officials already are sharpening their lobbying skills to joust with administration bureaucrats over the proposal, which would lop $158 million off school lunch subsidies annually across the country. For Washington area school systems, the loss would be above $2.4 million.

"It would be catastrophic," said Joanne Styer, director of the Montgomery school lunch program.

Like other cafeteria officials, Styer said the subsidy loss would lead to increases in lunch prices for students.

"And we know what happens when we raise prices -- for every one-cent increase, we have a loss in participation of one percent," she said.

Participation losses lead to job losses, according to McConnell, the Fairfax food director. "There is a scnowball effect of all this," she said.

Those backing the subsidy reduction include Carol Tucker Foreman, an assistant secretary of agriculture who notes that the nickel cut would affect only those children whose families earn $15,000 a year or more. As a general rule children in lower income groups are eligible for free or reduced-priced lunches. Subsidies for their lunches would not be affected.

In addition, Agriculture Department statisticians stress that the cost increase for a child's lunch would be only $9 a year.

Foreman said the money taken from the lunch program would be used to bolster the federal food program for low-income pregnant and nursing mothers and their infant children.

Arlington's effort to cut losses on its school lunch program began around 1971, according to Bailey McCrerry, a former marine who now runs the food service program for that school system. That was the year that the school board had to subsidize lunches by $437,000.

Officials decided to experiment with a central kitchen to see if it would help save money. Lunches are prepared in the kitchen and carried by truck to the school where they are reheated and served by one person.

The deficits quickly turned into profits.

The savings occurred primarily because of the reduced labor forces needed to prepare food in individual schools.

"Where we had four and five workers in the kitchen at one school, we now have one person who works three to four hours each day to heat the meals for that school," McCreery said.

Multiply that by 24 schools and the savings skyrocket.

At present the Arlington central kitchen serves only elementary schools. Junior high and senior high schools, whose students tend to be more demanding and to want more selections, still have their own cafeterias where food is prepared.

In the District of Columbia, the schools rely on two basic food service systems. One provides food prepared at the school site by the cafeteria workers each day. At Tameka Corley's school, for example, eight workers were on duty to prepare and serve 385 lunches. That compared to the one woman at Kim Lisa Sobotta's Arlington school who worked four hours to heat and serve 300 lunches.

Julius Jacobs, an official in the District's school food service program, said that the cost of labor has pushed up the District's meal preparation bills. "We pay more for our labor than other school systems -- we pay a miminum of $4.25 an hour," he said.

Despite the significantly higher cost to prepare meals in the District, the grumbling by students about the food appears to be as common there as in the neighboring jurisdictions.

At Eliot Junior High School in Northeast Washington, Nancy Wright and Carolyn Richardson, both ninth graders, poked at the meatloaf and noodles in a lunch that cost $1.54 to prepare. "Not enough seasoning," they pronounced.

They didn't touch the green peas on their trays and they only nibbled at the cornbread. "It's cold," Carolyn complained.

"Some days the food here is good," she said. "And some days it's not."