President Reagan's proposed federal budget cuts could cost Fairfax County up to $16.7 million in aid, but even if his ax cuts that deeply, county supervisors say they will continue to fight for a reduction in the county property tax rate.

County Executive J. Hamilton Lambert has proposed a county budget that would leave the tax rate at $1.54 per $100 evaluation, but because assessments have gone up an average of 14 percent, the typical homeowner's tax bill would increase by $168.

Lambert's budget proposal was presented before the county had fully calculated the potential impact of Reagan's proposed cuts. In earlier estimates, county officials had predicted the cutbacks would cost Fairfax $15.7 million in federal aid.

Even with the new estimate, presented to supervisors this week, board Vice Chairwoman Martha V. Pennino (D-Centreville) promised to continue to press for a lower property tax rate.

"We're going to have to find a way to cut the tax rate even if we lose federal aid," she said. "We have had a big increase in industrial growth, with all the new tax revenue that brings, and a big increase in assessments. We've got to find a way."

To make up for less federal money, Pennino said, "there will have to be adjustments." In other words, some federally financed programs run by the county may have to be scrapped or other programs will have to be cut.

Board Chairman John F. Herrity, a Republican, also predicted "there will be a cut in the tax rate," even if federal aid to the county shrinks.

If the aid cuts are deep, Herrity said, "We're going to cut programs we would not have funded except for the federal government. CETA (manpower training) is a perfect example."

Supervisor Thomas G. Davis III (R-Mason) joined Herrity and Pennino in predicting a tax rate cut despite the potential loss of federal aid.

The biggest potential loss to the county is impact school aid, which the federal government pays to the county for the education of children of military families and to make up for a loss of taxes from which the military is exempt.

But the county school system claims to have some new leverage in its long tug of war with Washington over impact aid. Under new state legislation, the county can back out of its contract of educate children of military personnel at Fort Belvoir.

Myron E. Cale, associate superintendent for financial services, said the school system collects $2.5 million from the federal government for the education of 1,520 Fort Belvoir children. But if Washington paid Fairfax what the county spends to educate nonmilitary children, Cale said, that aid would total $4.5 million.

That could mean a bill of almost $3,000 per child for the Fort Belvoir children, Cale said. He said he would assume the Army would pick up the bill, but if not, it would certainly have an adverse affect on military workers who might have to pay for their children's education themselves.

"If this won't affect the morale of military personnel," Cale said, "I don't know what will."

After impact aid, the second biggest possible cut in federal aid would be $4.5 million for school lunches. Without federal aid, Cale said, the price of school lunches -- now 60 cents at elementary schools and 70 cents at secondary schools -- would double. Board Chairman Herrity emphasized that all students, except the needy, should pay the true cost.

The third biggest cut in federal aid would be $1.5 million for education of handicapped, disadvantaged and adults.

According to the figures presented to supervisors this week, here are the specific funds losses to the county under the cuts proposed by the Reagan administration:

$8.4 million in impact aid.

$4.5 million in school lunch subsidies.

$1.5 million in school aid for the handicapped, disadvantaged and adult education.

$200,000 in manpower training money.

$200,000 in funding for the regional Health Systems Agency.

$1.8 million in mental health and mental retardation services.