Fairfax County Executive J. Hamilton Lambert proposed a $571.4 million budget yesterday that would raise nonschool spending only 6.1 percent, the smallest increase in recent county history and the first that is unlikely to keep pace with inflation.

The proposed fiscal 1983 budget, which calls for no tax increase, would nonetheless mean higher tax bills, since property assessments will go up by 10.5 percent. The tax bill on an average home would rise $142, from $1,351 a year to $1,493.

Lambert said the county treasury will be squeezed by federal budget cuts and the collapse of the housing industry, which provides most of Fairfax's tax revenue. Still, he said Fairfax can balance its budget without major program cuts or tax increases by limiting cost-of-living salary raises to 5 percent, using its work force more efficiently and depending on slowed but continuing growth in its tax base.

Lambert recommended that the Board of Supervisors maintain a property tax rate of $1.51 per $100 of valuation and estimated that the median value of a home will rise from $89,455 to $98,848. His general fund budget of $571.4 million is up 10 percent from this year's $519.6 million, but the School Board requested the bulk of the increase.

The county executive by law must pass on the school board's request for local funds--in this case, $288.6 million or 14.6 percent more than this year's contribution. But the nine elected supervisors, who will consider the budget in March and hold public hearings in April before adopting a tax rate two months from now, may cut the school proposal.

Board Chairman John F. Herrity said he will vote to cut the appointed school board's request. "It's absolutely the biggest slop bucket I've ever seen," he said, adding that overall school spending should not grow by 10 percent while student enrollment declines.

"The problem is that we have decline in some areas and growth in others," school department spokesman George F. Hamel said. "And the overhead of a facility remains the same whether you've got 210 kids or 200 kids." In addition, federal aid to the schools is expected to drop by about one third.

The 6.1 percent increase in general-fund spending compares to an increase of nearly 11.9 percent in 1982 over last year. Last year, however, employes received a 9.1 percent cost-of-living raise, and Lambert acknowledged that the proposed 1983 raise of 5 percent will not keep pace with inflation.

Lambert actually proposed spending a total of $908.9 million, up 2.1 percent from the current year. That figure includes school and nonschool spending, plus the costs of bond funds for construction projects and other costs not supported by local taxes. The total figure does not offer an accurate picture of government growth, since it includes one-time costs like the building of the county courthouse.

Lambert also recommended that the supervisors establish a permanent 2 percent reserve because of the unpredictability of the economy and of federal and state budget actions. "I can't recall when there has been such uncertainty in the preparation of the budget," Lambert said. Congress will still be debating its budget next fall, while the county fiscal year begins July 1.

The recession has hit hardest the county's two chief sources of revenue, housing construction and new car sales. County officials project a 14 percent growth in the tax base in 1983, compared to 20 percent this year, and they said the problem will worsen in 1984 because assessments tend to lag about two years behind market values.

Lambert said he wants to take advantage of the recession by starting as many construction projects as he can while builders are hurting for business. Despite the mood of fiscal austerity, the county--with a population expected to grow from 600,000 in 1980 to 644,000 by the end of this year--is building three new fire stations, two regional government centers, two regional and one branch library and several major road and sewer projects.

"Our whole thrust has been to expedite these projects as much as possible and get them out to bid and take advantage of the economy," Lambert said.

Those plans could be thwarted by high interest rates, however. The county, although it has maintained its AAA bond rating as a creditworthy customer, must pay about twice as much to borrow funds as it paid two years ago. Lambert said the board may have to consider spending more tax revenues on construction projects.

The county will receive about $42.7 million in federal aid this year, down from $50.6 million in 1981. Officials are counting on just $28 million in 1983--with the biggest reductions expected in school and housing programs--but they said they really do not know how much aid to expect.