The lawyers on the Houston case had just left the leafy peace of Lawrence Grossman's house in Bethesda to file the brief in behalf of the Texas affiliates' right not to show "Death of a Princess."

The lawyers on the San Jose case would wait until morning to argue against the suit filed by an irate citizen who claims that airing the film would bring on nuclear holocaust.

It was only early this weekend that the much beleaguered president of PBS returned from Las Vegas, after appearing on one of his commercial competitor's programs to explain why PBS was airing the film in the first place.

Lawrence Grossman should be looking very frazzled by now, Congressmen very influential in the funding of PBS have thundered against the program. Mobil Oil, which shells out $3 million to public broadcasting, has been paying big bucks for newspaper advertising against it. There have been letters of protest from Saudi Arabia and a cover letter from the State Department disclaiming any attempt at censorship. Grossman looks about as frazzled as a glass of ice tea.

"If the fate of nations rests on the showing of one television program, then the problems we're facing are far greater than that of the show itself," he says in relaxed tones that go well with the standard Sunday casual look of old cardigan and blue jeans he's wearing. "Our job is to be in broadcasting, not to make foreign policy."

Still, it is not as if there have not been foreign policy implications in the showing of "Death of a Princess." A "docudrama" of the 1977 execution of a Saudi Arabian princess and her alleged lover for adultry, the program's presentation in Great Britain resulted in the departure of Britain's ambassador to Saudi Arabia, a ban on the landing of British Concordes in Saudi Arabia and a full-scale review of the state of relations between the two countries.

Grossman, of course, is aware of the recent history, the British uproar having prompted him to bring a copy of the film home to screen for himself for the first time.But this did not, he says, play into his decision on whether or not to present the program to PBS's affiliates.

"If we had received any communications from the State Department saying, 'we're not telling you what to do but the airing of the program will have serious consequences,' then we would certainly have taken that into account," Grossman says. "But that didn't happen."

There have been thousands of calls, of course, both to the individial PBS affiliates as well as to Grossman. The calls basically arrange themselves in two categories. There is the death of Western civilization point of view, expressed in former Joint Chiefs of Staff chairman Thomas Moorer's comment that he would see Grossman in the gas lines that would result when Saudi Arabia cut off the oil in retaliation.

And at the other end of the spectrum are the encouraging words from the prominent network newsman that called yesterday, to the words of support from congressmen like Albert Gore (D-Tenn.) and James H. Sheuer (D-N.Y.).

At any rate, Grossman says, the pendulum of public opinion has been swinging toward support of PBS while Grossman's support of the program itself, he says, has never wavered.

"The dramatization is troublesome," Grossman said. "I don't usually consider it a responsible way to present a news program. But first of all there was no other way to do this event, since the participants are obviously no longer with us, and secondly, we are not saying there is only one way to look at what happened or to interpret it.

"As a matter of fact there were two sources for every piece of information and we have taken great care to present the program in such a way that puts it in a context, a perspective. I think it's a very well done program. I'm very proud of it.""

Despite the nonchalance with which Grossman discusses the brouhaha that has surrounded him, the clamorous ways in which events have converged on him did strike a chord as he emerged from presenting his case live on network television only to go off to dinner in the center of America's neon nervous system, Las Vegas. "There we'd been, dealing with all these cosmic questions, only to emerge back into the glitter and the madness," he said. "Maybe that's the ultimate reality -- inconsistency and irony."

The controversy followed Grossman around the country as he traveled to Chicago, Atlanta and Las Vegas, visiting with affiliate station directors, in a previously scheduled round-robin of talks. It was at the Chicago airport that Grossman got a protest letter from the Saudi government and the disclaimer from Warren Christopher, then acting secretary of state.

While Grossman has replied formally to the Christopher letter, he is not sure whether any response will be made to the ads that the Mobil Oil Corp., partners with the Saudis in the oil business, has run in major newspapers urging PBS to "review" its decision to air the program.

Grossman is particularly irritated by the Mobil ads, though he doesn't believe that the corporation's opposition will have any effect on their funding of PBS programs. Still, Grossman recalled an earlier offer Mobil made to network television to pay for the ads of opposing groups if they could be allowed to state their own case on the air. Perhaps, Grossman suggested, Mobil might be willing to buy newspaper space for PBS to state its side of the case in the "Princess" issue.

"In a funny kind of way, my whole life's career has been like this," says Grossman, a former advertising executive with both CBS and NBC who operated his own public relations firm until his election as president of PBS in 1976. "During the Kennedy assassination, when I was vice president in charge of advertising for NBC, there was the question of if to promote, and if so, how and what products, during the coverage." Later, he helped to organize an application for a commercial TV station in New York after former members of the news department there claimed that the department was distorting the news it broadcast.

Grossman also recalls the furor raised when PBS' predecessor, NET, aired a documentary film on what was then called North Vietnam that 33 congressmen had petitioned to ban from the air waves. "The program was aired and the world didn't come to an end," Grossman says. "And it won't this time . . . As long as we're being hit from all sides, it can't be too bad."