Mayor Marion Barry yesterday asked for a $36.3 million increase in the District's 1982 budget, including funds to open an additional jail facility at Lorton, hire 167 more security guards for it, establish the city lottery approved by the voters last November and set up a statehood constitutional convention.

The mayor's amended 1982 budget would raise total spending to $1.55 billion.

But despite the city's fiscal crisis and acute cash shortage, Barry assured City Council Chairman Arrington Dixon that no tax increases would be required to fund the money bill. Rising prices, property values and incomes have resulted in anticipated increases in sales, real property and income tax revenues that are almost enough to cover the additional spending, Barry said.

The mayor's proposed amendment to the 1982 budget is perhaps more notable for what it leaves out than for what it includes.It contains no additional money for salary increases for city workers, even though the mayor said he recognizes that the funds in the original budget will not be enough to cover what the workers will probably win in negotiations now under way. Nor does it contain enough money to meet the city's obligations to the pension funds for teachers, police officers and firefighters.

Both costs, Barry said, will have to be met out of revenue sources not currently available, probably an increase in the annual federal payment.

The budget contains only $16.8 million for salary increases, approximately enough for a 2 percent pay raise, and even that was inserted into the original budget by the City Council over Barry's objections. In a letter to Dixon accompanying the budget amendment, Barry said, "even though I know that the $16.8 million . . . is not enough, it is not advisable to add anything at this point. To do so would be a disservice to the newly established collective bargaining process."

On the pension funds, which have become a persistent irritant to the mayor and his financial advisers, the mayor included an extra $4.9 million, bringing the total pension budget for 1982 to $133 million. But that is at least $10 million less than will be required after actuarial recomputations have been completed.

If full funding for the pensions were included, Barry said, "we would have to choose not to fund street lighting, schools, emergency ambulance services, disability and unemployment compensation, social services and low and moderate income housing needs.

"I have elected not to delete these programs," he said. "My administration would never abandon its commitment to those who need the government's services the most."

The city government is required by law to meet, on time, its full obligation to the retirement funds. Both the federal Office of Management and Budget and the D.C. Retirement Board, which is the custodian of the funds, have been demanding complicance. The mayor said yesterday that his action in keying the payments to an increased federal payment "should in no way be interpreted as an indication that we will not meet our responsibilities."

The key items of the revised budget include:

An increase of $5.6 million, to $78.1 million, for the Department of Corrections. Most of the money would be used to convert part of the Alcoholic Rehabilition Center at Occoquan, adjacent to Lorton, into a medium-security detention facility for 400 inmates. A spokesman for the department said the facility would house "convicted misdemeanants," persons convicted of crimes for which the maximum penalty is less than a year in jail. The department's staff would be increased by 194 workers, of whom 167 would be guards.

An allocation of $628,000 to begin operations of the Lottery and Charitable Games Control Board. That agency, which will have a staff of 19, will set up and run the lottery and bingo games approved in November's referendum.

A $700,000 fund to hold a convention to draft a state constitution for the District, which also was approved by the voters, and to promote the concept of statehood.

A fund of $2 million to cover administrative costs associated with one of the most ambitious schemes ever undertaken by the District government: the sale of $100 million in revenue bonds to raise mortgage money for homebuyers. The bonds, if sold, would be repaid from the proceeds of the mortgages. Since the bonds would be exempt from federal taxation, they would carry an interest ratge well below market, enabling the city to make more low-cost mortgages available.