Metro general manager Theodore C. Lutz proposed yesterday a $237 million operating budget for fiscal 1980 that would inaugurate subway service on Sundays, shorten the waiting time between trains and cost taxpayers $23 million more to operate the system than it does this year.

Lutz proposal for the combined bus and subway system will now be submitted to months of intensive review by the area's legal governments and the Metro board.

The budget's recommendations envision improved service as well as expanded service, because by the end of fiscal 1980 the subway system will have 10 more miles of line in operation and will extend to Glebe Road and Fairfax Drive in Arlington County to the New Carrollton Triangle in Prince George's County.

The budget proposal represents a 13.8 percent increase over the operating costs for the current fiscal year, which ends next June 30. But the subsidy requirement - the different between the operating costs of the system and the revenues it collects - is projected to increase by 23 percent from $98.8 million to $121.7 million.

Even that increase assumes that the Metro board will increase fares next July 1 by an average of 3.5 percent, which is estimated to be half the rate of inflation.

Even that modest fare increase, however, is certain to be controversial because each increase costs Metro some riders. "If the costs of competing services - the automobiles - were not being artifically held in place," Lutz said, "there would be less problem with transit fare increases."

Gasoline and parking prices - two key factors in an individual's decision whether to drive or ride - have stayed fairly constant here. Much parking for federal employes continues to be heavily subsidized.

Sixty percent of Lutz's proposed budget and two-thirds of the subsidy required are for the bus system. While the subway is continually reaching out into the metropolitan area the bus system remains the largest carrier in the region. But its character is being changed to that of a feeder service for the subway.

Lutz's budget estimates that it costs Metro $1.25 to carry a rider on the bus, but $1.15 to carry him on the subway. Subway advocates have held that long-term subway operating costs would be cheaper than long-term bus operating costs and thus offset the heavy construction costs of the subway.

The budget envisions an increse of 240 employes, almost all of them in the rail operations or support areas. There is a decrease in the size of the bus fleet and in the number of people needed to run it.

Lutz attributes about half the increase in the budget to simple inflation, the rest to other factors, primarily expansion of service.

The problems that his budget is going to have were obvious from the comments of Joseph S. Wholey, Metro board chairman and a member of the Arlington County Board.

"Clearly Metro is expanding, so the increase is somewhat understandable," Wholey said. "Still, the local governments, wishing to have police and fire services and public schools, will have to think twice about giving 20 percent increase to one and only 2 percent to somebody else."

Lutz specifically proposed 16 hours of Sunday subway service, between 8 a.m. and midnight. It would start either Sept. 2 or Sept. 9, 1979, depending on "which weekend the Redskins open at home," Lutz said.

He also proosed that rush-hour intervals between trains be reduced from six minutes to four minutes on the Red Line and from six minutes to five minutes on the Blue Line.

Lutz' budget also include an appeal for special taxes in Maryland, Virginia and the District of Columbia that would be dedicated to Metro and thus take the Metro burden off the property tax.

Without such regional funding sources. Metro must suballocate its costs to eight separate area governments under a complex set of formulas. That process, Lutz said yesterday, "enhances divisiveness."