The Arlington County School Board has asked the county board to finance nearly $1.5 million in capital improvements in fiscal year 1982, including $922,600 for renovation of Washington-Lee High School.

The Washington-Lee project, as approved by the school board last month, would cost a total of $1.9 million. The school board is seeking a $1 million loan from the state's "Literary Fund," a revolving fund for school construction projects.

But the Arlington County Board, which must approve the school board's application for the loan, has refused to do so. The school board has asked the county board to reconsider its decision.

Renovation of the 28-year-old science wing at Washington-Lee should be given top priority, the school board agreed at its meeting last week.

Opponents of the renovation have challenged the cost and necessity of the project, arguing instead for less expensive, phased-in repairs. In a letter to the school board, County Board Chairman Walter L. Frankland suggested that the project may not be necessary because of the possibility of future consolidation of the county's three high schools.

But O. U. Johansen, school board chairman, replied in a letter to Frankland that it would be several years before declining enrollments possibly force a high school to close. Even then, school officials have said, Washington-Lee may be used for community or other school programs.

Phrasing in the repairs would cause more disruption for the students and would be more expensive because of inflation, Johansen argued.