Acting Fairfax County Executive J. Hamilton Lambert proposed yesterday an election-year budget that would boost the average homeowner's tax bill by about $93 a year and fund a 10 percent increase in spending largely from higher real estate tax assessments.

Lambert's $628.1 million budget for the fiscal year begining July 1 would keep the county's property tax rate at its current level but since the value of the typical Fairfax home has jumped 8.3 percent, few homeowners will receive lower bills next year under the Lambert budget.

If county supervisors, who face election this fall, accept his proposal, owners of the county's median-priced homes -- valued at $68,200 in 1978 -- will pay $93 more next year.

Fairfax Board Chairman John F. Herrity said he expects the supervisors will cut the current real estate tax rate below that recommended by Lambert. But even if the board adopts a cut as sharp as the maximum suggested by Herrity, the average homeowner is likely to face a higher tax bill because of increased real estate assessments.

Lambert said his budget calls for no new county programs and keeps "increases to the minimum amount necessary" to continue "the current high level of service" that the county govenment provides.

The only dramatic increase in the budget is a 50 percent jump in funds that the county must pay as its share of the Metro transit system. The amount would climb to $12.1 million next year from $8 million in the current budget, an increase that officials said reflects a new cost-sharing formula that falls more heavily on the county.

Lambert's proposal would grant a 5.15 percent pay increase to all 20,500 county employes, including schoolteachers.

Neither county employes nor supervisors appeared yesterday to be happy with Lambert's proposal. Employe groups called the salary increase too small and some supervisors predicted they will cut the real estate tax rate below the level that Lambert recommended.

Board chairman Herrity said he expects the board wil attempt to cut the tax rate, currently $1.64 per $100 assessed value between 5 and 10 cents.

Even if the board manages a cut of 10 cents, many homeowners in the county would fail to see a decrease in their property taxes because of higher assemssments. The owner of that median-priced Fairfax home would pay $20 more in real estate taxes next year even with a 10-cent decrease in the tax rate.

"We've had a terrific tax increase over the past three years with this board," said Carl Ericson, president of the Fairfax County Federation of Civic Association, a group that monitors county spending proposals. "We will be taking a tough look at this budget to see if the tax rate could be cut 15 to 20 cents."

Funding for schools -- $180.9 million -- represents the largest item in the county's operating budget. Kambert said the county's school financing is 12 percent higher than the current year because of a decrease in state and federal funding for schools.

Lambert defended the proposed increases saying that they are based on the president's pay increase guidelines of no more than 7 percent.

"We don't think it's enough to cover the increased cost of living," said Pete Moralis, president of the Virginia chapter of the American Federation of State, County and Municipal Employes, which formerly represented 3,000 county employes before collective bargaining agreements were banned in the state. "We would like to see more."

Lambert's budget depends partly on the surge in housing and commercial construction in the county for new revenue. New property listings account for 38 percent of the county's increased taxes under the Lambert proposal. Reassessments on existing buildings and housing account for the other 62 percent.

More than of the $628.1 million budget would be raised by county real estate and personal property taxes. Those taxes account for $343 million of the county budget. State funds provide another $86 million, and $32 million comes from federal sources.

The remainder of the county budget is financed from county fees, licenses permits, bond sales and other sources.

James P. McDonald, deputy county executive for management and budget, said the proposed level of spending would place the county "in a very sound financial posture."