Theodore C. Lutz, who resigned as Metro general manager last April because, he said, he was "burned out," is Transportation Secretary Neil Goldschmidt's top choice to head federal mass transit programs. The Washington Post learned yesterday.

Lutz's name has been submitted by Goldschmidt to the White House for consideration, and Lutz has told Goldschmidt he will take the job if it is offered.

Lutz held the top budget job in the U.S. Department of Transportation under two Republican secretaries in the Nixon and Ford administrations and that fact is seen in some circles as a potential problem with the Democratic White House.

Lutz was replaced at Washington Metro by Richard S. Page, who then held the job that Lutz would take as head of the federal Urban. Mass Transportation Administration. In other words, Page and Lutz would be switching jobs if Lutz's appointment goes through.

When Lutz, 34, left Metro in April he said that he was exhausted, "burned out" by 2 1/2 years of wrestling with Metro, and that he did not have enough time for his family. He questioned whether the public was putting an unreasonable burden on its top administrative officials.

Yesterday, in a telephone interview, he sounded as if he could not wait to get back to work. He talked enthusiastically about what needs to be done at the federal transit agency and about Goldschmidt, who has a record as a strong mass transit advocate.

What changed Lutz's mind"

"I had my four months [off] and I did what I wanted to do, " he said, "I visited my folks. It's time to go back to work, and I'm public-service oriented.If they ask me to do it, I'll do it. I think that agency needs some stability."

Lutz knows the federal transit agency and its problems well both from the federal and local perspective. Furthermore, the agency is a part of the Deparmtent of Transportation, and Lutz had said to friends that his former position as the top budget officer was "the best job I ever had."

Lutz held the rank of deputy under-secretary, and it has always been an open question at the department whether the assistant secretaries or the administrators outranked each other. There has never been any question that the budget officer was more equal than anyone else.

No one has replaced Page since he left the agency for Metro in April, a fact that has disturbed mass transit leaders around the country. In the summer of the Big Gasoline Crisis, when commuters rediscovered and quickly overburdened existing public transit facilities in big cities on both coasts, there was nobody in Washington strongly pushing the federal grant program.

The problem was exacerbated with the departure of Transportation Secretary Brock Adams, who was fired by President Carter during the recent cabinet shakeup. Adams charged that the administration had been less than enthusiastic about mass transit.

Part of the Carter administration's new energy proposal includes a windfall profit tax on oil companies.A total of $13 billion from that tax over 10 years would be devoted to public transit rehabilitation and expansion programs, a figure that more than doubles the current federal program level.

Goldschmidt, the former mayor of Portland, has not been confirmed as secretary yet and holds a "recessed appointment." His confirmation hearing with the Senate Commerce Committee is scheduled for today.

Goldschmidt and Lutz got to know each other well this past summer when both were on a tour of European cities and transit systems. The tour was sponsored by the National League of Cities.

Lutz remained in Europe after the tour to do some private traveling with his wife, Willa, and their one-year-old son Christopher. "I got back and discovered that Neal Goldschmidt was the secretary-designate," Lutz said. "He called me and said that he needed somebody good to do this. I said, "Well, I'd consider it,' Right now, any further word would have to come from the White House.

The White House did not return a telephone call yesterday. A Transportation Department spokesman said that "Ted Lutz is probably the outstanding person in public transit today but any announcement of appointments would probably come from the White House in the future."

If Lutz gets the position, he will take a pay cut, a fact he professed not to know yesterday, "I don't even know what the job pays," he said.

The transit agency administrator gets $52,500 annually. Lutz was paid $58,000 by the time he left Metro and Page is receiving $60,000. Lutz twice turned down salary increases at Metro.