The Fairfax Board of Supervisors yesterday awarded a 5 percent raise to County Executive J. Hamilton Lambert, whose current $70,000 annual salary makes him one of the highest-paid local government officials in the Washington area.

The board also voted 5 percent pay raises for Lambert's three deputies, who earn between $55,000 and $69,000. The actions came two weeks after the board adopted a 1982 budget that gave 5 percent cost-of-living raises to all county employes except the top managers.

Supervisors said yesterday they forgot to include Lambert and his deputies when they adopted the budget.

The supervisors also asked three community leaders to study whether the next county board, to be elected in 1983, also deserves a pay raise. Most supervisors now earn $19,961 per year, and are scheduled to get $20,759 after July 1.

The nine elected supervisors appoint the county executive, who is the full-time manager of the growing county bureaucracy. The executive's salary became a political issue earlier this year when the board considered a consultant's pay plan that could have increased the top four executives' salaries to more than $86,000 within two years.

The board shelved that plan, leaving Lambert's salary at $70,000 plus $4,500 in fringe benefits. His deputy for budget and finance, James P. McDonald, earns $69,000 plus $1,750 in retirement benefits and transportation allowance.

Top-level presidential appointees, including Cabinet secretaries, earn a maximum of $69,630.

Metro General Manager Richard S. Page earns $73,401 and D.C. Mayor Marion Barry earns $64,000 per year, as does the chief administrative officer of Montgomery County, Robert W. Wilson. Virginia Gov. Charles S. Robb earns $75,000 and Maryland Gov. Harry Hughes is paid $60,000.

The board voted 7 to 0 for the raises for Lambert, McDonald and Deputy County Executives Verdia Haywood and Richard King, who earn $55,904 and $67,952, respectively. Board Chairman John F. Herrity was not in the room during the vote and Joseph Alexander was absent from the meeting.