Alexandria City Manager Vola Lawson proposed a tight $155.7 million budget yesterday that asks the City Council not to cut real estate property tax rates and falls $1.5 million shy of what the superintendent of schools has requested.

The proposed budget for fiscal year 1987 beginning July 1 gives city employes a 4 percent salary increase, raises the Metro subsidy 22 percent to absorb federal transportation cuts, and creates 82 new jobs, mostly for deputy sheriffs needed to guard the almost completed 400-bed jail.

"In this year of substantial federal funding uncertainties," Lawson said, "it's a realistic budget."

The property tax cut that the City Council said six months ago was likely, now would not be prudent, Lawson said. But a $1.8 million fund set aside in the event of deep federal cutbacks could be refunded to taxpayers if it is not spent.

The council, facing its bitterest funding dispute with school officials, is scheduled to vote on the final budget draft May 5.

"It's pretty desperate," said School Board Chairman Lou Cook, about the need to get $1.5 million more from the city than Lawson recommended. "We're going to have to increase the size of classes and rif teachers."

In addition, Cook said summer school classes would have to be dropped and the average 7.7 percent salary increase promised to teachers rescinded.

"I'm not above dropping leaflets all over town," she said, promising to put a "big effort," into persuading the elected officials to meet the schools' $59.9 million budget request.

Mayor James P. Moran Jr. called Lawson's budget "responsible and responsive."

Because Alexandria already spends more per pupil than Fairfax and Arlington counties, he said, "I can't imagine they [school officials] would expect any more money."

If the real estate property rate remains at $1.39 per $100 assessed value, as Lawson requests, the average homeowner would pay about $105 more next year because property values rose 6.4 percent.

The average single family home valued at $118,900 last year is now worth $126,500, according to the city assessor.

For public transit, the city also will have to pay more.

Drastic reductions in federal and state funding for the Metro means Alexandria will have to pay $1.3 million more, or a total of $7.3 million, for rail and bus service, according to Lawson.

The new Public Safety Center, however, is expected to bring some new revenue from the federal government. Located near the Eisenhower Avenue Metro station, the $26 million complex, which includes a 400-bed jail, will be open to federal prisoners on a perdiem basis.

Sheriff James Dunning said the federal government already has paid $2.6 million toward the capital costs of the complex and will pay an average of $80 per day for each prisoner kept in the facility.

Lawson said she expects as many as 200 federal prisoners to be housed in the center.

Lawson also outlined a six-year, $66.7 million capital improvement program that centers on repairing roads, bridges and public schools. That is considerably lower than the proposed capital outlay for last year, which was $86.6 million.

To encourage economic development, she also listed among her immediate priorities:

*$307,000 for Cameron Run Valley, to finance the completion of the Bluestone connector road and the widening of Duke Street from Longview Drive to Wheeler Avenue.

*$575,000 to revitalize the Mount Vernon Avenue corridor by improving landscaping, streets and signs.

*$259,000 to spur the redevelopment of Arlandria, where run-down housing threatens to leave 3,000 of the city's poorest residents without homes.