The Fairfax County Board of Supervisors awarded County Executive J. Hamilton Lambert a 10 percent pay raise yesterday, increasing his salary to $87,439 a year and making him the highest paid local government executive in the Washington area.

"Jay gets offered a job every week," said board Chairman John F. Herrity. "We have to try to be fair."

The board's unanimous decision came barely a month after Fairfax School Superintendent William J. Burkholder announced his resignation because of public outcry over the School Board's decision to give him a $157,250 annual benefit package. That included a yearly salary of $79,450 and an annual compensation of $77,800 for retirement benefits he would lose by remaining in the job.

"At least Lambert's is more modest than that," said Herrity. "This doesn't sound like an outrageous salary to me."

The board's action increased Lambert's salary from $79,450 a year to $87,439. The pay raise is retroactive to July 1.

Even at his previous salary, Lambert was paid more than other officials in equivalent positions in the metropolitan area. His salary now is $12,900 a year higher than that of D.C. Mayor Marion Barry and about $14,000 more than the pay of Maryland Gov. Harry Hughes and Virginia Gov. Charles S. Robb.

"He's been offered salaries in the private sector double what we're paying him," said Herrity. "This is peanuts compared to what he could make in the private sector."

Board members said the raise came several months after the county's routine budget review because a board subcommittee has just completed a salary study of top local government officials. As to the timing, Lambert, 43, said: "Any time you do it, it'll be a problem."

Board members said they increased the salary partly to provide more balance between Lambert's salary and those of his deputies, two of whom are paid $78,355 a year.

Officials also praised Lambert's four years as county executive. Lambert worked his way through the county government ranks from a map draftsman in 1959 to county executive in 1980.

"He has been doing an outstanding job," said Supervisor James Scott, who is a Democrat. Lambert serves in the position at the discretion of the board rather than under a contractual arrangement such as the school superintendent has with the School Board. The county provides Lambert with an automobile.

The supervisors also filled a two-year vacancy in the county's public works department yesterday. John W. Di Zerega, a 13-year county employe, was named director of the office at a salary of $70,109.