A House-Senate appropriations conference committee yesterday agreed to bail out financially strapped St. Elizabeths Hospital with an additional $5.7 million in federal funds, but warned that this is the last time such aid for the hospital will be forthcoming.

St. Elizabeths has been facing a $25 million shortfall in funding for fiscal 1984, which hospital officials had feared would require massive staff layoffs, sharp program cuts and loss of accreditation if neither the federal nor the city government came through with the funds.

Yesterday's action finally closed the budget gap, after the federal government came up with a plan to save $14 million in administrative costs and the city agreed to take 289 St. Elizabeths patients into District nursing homes and community facilities to save another $5.3 million at the hospital.

In completing work yesterday on the District's fiscal 1984 budget, the conference committee agreed to a total of about $31 million more in federal funding than originally planned, mainly for initiatives in the criminal justice system to relieve overcrowding at the D.C. Jail.

But the District's budget headaches are far from over. The city government already has had to cut back sharply on programs for this fiscal year and next, and now it must deal with a number of costs it had not anticipated when it first submitted its fiscal 1984 budget.

These include $12 million in streetlighting costs that the city had hoped to shift to utility consumers--a move that cannot be accomplished quickly if at all, another $10 million the conference committee decided the District must find to help pay off its long-term deficit, and a recent $4 million agreement for pay raises for the city's court-appointed trial lawyers.

There will have to be "an awful lot of budget adjustments" made in the fiscal 1984 spending plan to accommodate these elements, said D.C. Budget Director Betsy Reveal.

The conference committee yesterday agreed to add $22.3 million in federal funding for the D.C. corrections system, as approved by the Senate in its version of the budget. This is to go toward finding and renovating facilities in the District as minimum-security prison space in order to get prisoners out of the overcrowded D.C. Jail; additional corrections staffing; and educational and vocational training programs aimed at first-time offenders.

Another $2.8 million was approved to add seven judges to the 44-judge Superior Court and for capital improvements at the courthouse, subject to approval of a separate authorization bill that would have to go through other congressional committees.

Sen. Arlen Specter (R-Pa.), Senate D.C. appropriations chairman, said he hoped that the D.C. criminal justice system, particularly with the newly approved education program, could serve as a "model for the nation."

While city officials have welcomed the extra funds and support the initiatives, they also present a potential future problem because the city will have to find a way to fund the new programs if they are to continue.

"We will have to take a hard look at the future-year impact of any initiatives approved today," Reveal said. "An increase in the operating base is problematic."

Rep. Julian Dixon (D-Calif.), chairman of the House D.C. appropriations subcommittee, said the criminal justice initiatives will mean ongoing expenses to the city of about $10 million a year.

The conference committee also approved funding for a study of a controversial merit-pay system for District teachers, but cut the amount from the $1.5 million the Senate had approved to $350,000.

As approved by the conference, the city's $2.2 billion budget would include federal funds of about $600.8 million.

The conference report is expected to go to the House and Senate floors for final congressional approval next week.

The federal government's plan for saving $14 million at St. Elizabeths will have to include staff layoffs, but far fewer than the 906 once predicted, according to a federal spokesman. It will also include consolidation of wards that are operating at less than capacity, changes in the phone system, and attempts to reduce the length of stay for patients, he said.

The city plans to deinstitutionalize about 200 St. Elizabeths patients by April 1, and it plans to take over the drug and alcohol programs for 89 patients now in the hospital by midyear.

In suggesting that the appropriations bill include the other $5.7 million needed at the hospital, Dixon expressed disappointment that the shortfall problem had not been resolved by federal and city officials in some other way.

"Nowhere at any time will we give more money to this program to bail it out," he declared, asking that language be added to specify that in the conference report.