The free lunch is over -- at least for 1,233 students in Fairfax County schools, as well as a "handful" of children in Arlington and Alexandria.

This week, under a plan proposed by the Carter administration and approved by Congress in December, children from some low-income families who had received free lunches began paying 20 cents for delicacies like those on Monday's menu in Fairfax: "thinly sliced turkey piled high on a sesame seed roll with potato rounds, lettuce, tomatoe, pickle, onion. . . ."

The full price for the lunches in Fairfax is 60 cents at elementary schools and 70 cents at secondary schools.

In Arlington and Alexandria, officials say they did not know how many students were now paying for part of their lunch costs or had been eliminated from the federally subsidized program altogether since principals at each school, not the central administrations, had notified parents whose children were affected by the changes. School administrators in both systems, however, said they believed only a "handful" of children were affected.

The new requirements, part of former President Carter's efforts to trim $90.4 million from the federal budget, are expected to affect about 450,000 children, who will be required to pay for part or all of thier school lunches.

Under the changes, families will no longer be able to adjust their net income to compensate for exceptionally high costs of living. Local officials say the areas they expect to be hardest hit are urban centers such as metropolitan Washington and New York City, where the cost of housing and food far exceeds the national average.

The changes mean that a family of four can have a gross income of no more than $10,270 a year to qualify for the three lunch program. Under previous regulations, a family of four earning above the limit could still qualify for free lunches because of income adjustments made when expenditures for housing, medical needs or special education totaled more than 30 percent of their yearly income.

In Fairfax County, most of the students affected by the changes come from homes where gross annual incomes are between $10,271 and $15,490. In the past, when their incomes were adjusted for exceptionally high living costs, most of those families qualified for free lunches; under the new rules, those families may still be eligible for reduced-price lunches. In addition to children paying reduced prices, Fairfax officials said 14 county children have been eliminated from the program.

School officials point out that the Reagan administration strongly supports the new regulations and is considering the new regulations and is considering tightening the measures further.

"I think this is just the first step," said Dorothy Pannell, director of food services for the Fairfax schools. "Mr. Reagan is probably going to recommend even more cuts."