Fairfax County Executive J. Hamilton Lambert got a 3 percent pay increase yesterday from the County Board of Supervisors, a day after the School Board approved a 5 percent increase for Superintendent Robert R. Spillane.

The actions will raise Lambert's annual salary to $129,348 and Spillane's to $116,550, making them the highest-paid employees in the county and among the highest-paid in the nation in their fields.

Because he works under contract with the board, Lambert was the only county employee who was not included when the supervisors approved a 3 percent cost-of-living increase for county workers as part of the fiscal 1991 budget. Salaries for Spillane and his top aides are decided separately by the School Board, which gave teachers a 3 percent cost-of-living increase this year.

"I think it's appropriate that the same cost-of-living increase be given to top officials as everybody else," said Board of Supervisors Chairman Audrey Moore, saying that "the County Board's actions were more appropriate" than the School Board's because all county employees received the same percentage increase.

The Board of Supervisors and School Board have gotten into an occasional salary competition between their two top employees. Spillane also receives a $10,000 annual retirement annuity, but Lambert remains the highest-paid county employee.

The cost-of-living increases go into effect July 1 and will increase Lambert's pay $3,767 and Spillane's by $5,550.

The board approved Lambert's raise on a 6 to 2 vote, with Republican supervisors Thomas M. Davis (Mason) and Elaine N. McConnell (Springfield) voting against the raise. Supervisor Joseph Alexander (D-Lee) was absent.

"I think both these guys {Lambert and Spillane} get paid enough," said Davis, adding that Lambert got two salary increases last year. "They're paid amply, particularly at a time when taxes are being driven up and services are being cut."

"I made a commitment to vote against all these high salary increases," said McConnell, adding that the county residents think local government employees are paid too much.

Spillane's increase was approved in a 6 to 3 vote Sunday and will be confirmed at the School Board's June 14 meeting. The vote reflected Spillane's support on the board, with "no" votes from Laura I. McDowall (Annandale), Letty A. Fleetwood (Providence) and Robert E. Frye (At Large), all frequent critics of the superintendent.

McDowall said her vote was "based on performance," but would not elaborate. Fleetwood could not be reached for comment. Frye, who called for Spillane's resignation last year after a racially charged public confrontation, said "no pay increase was deserved."

Lambert's salary has been a frequent source of controversy. In arguing that county spending is out of control, tax protesters and budget cutters often complain that Lambert is paid more than the vice president and the chief justice of the United States. Spillane's benefit package would put him in that category, too.

According to a salary review of local government officials in the September edition of City & State Newspaper, Lambert was the highest-paid county executive in the country. Two county officials in the nation, according to the review, made more than him: the administrator/managers of Los Angeles and Dade (Miami) counties, who received $138,000 and $123,000 respectively.

At the time of the survey Lambert made $122,398. No more recent comparison figures were available. In January, Lambert's salary was raised to $125,581.

Spillane used to be the highest-paid superintendent in the area, but now trails Prince George's County schools chief John A. Murphy, who is paid $120,000 a year.