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A conservative lobbying group is locking horns with the Reagan administration over whether members of the alleged Walker family spy ring should face the death penalty. Paul D. Kamenar of the Washington Legal Foundation says government prosecutors have already ``thrown in the towel'' by refusing to press for possible death sentences for Arthur, Michael, and John Walker. But Mr. Kamenar hopes the government will shift its strategy in the coming trial of Jerry Whitworth, who is accused of supplying Navy buddy John Walker with sensitive US documents to sell to the Soviets.

A federal judge in San Francisco will receive written arguments Monday on whether the death penalty should apply in the Whitworth case. The judge will hear those arguments in court Friday. (The last Americans to be executed for espionage in the United States were Julius and Ethel Rosenberg, in 1952. They were convicted of turning over atomic-bomb secrets to the Soviet Union.)

US Attorney Joseph P. Russoniello, who is handling the Whitworth case, declined to comment on the death-penalty issue last week, saying only that the government's stance was being determined in Washington.

According to James Larson, one of the lawyers defending Mr. Whitworth, the government is no longer opposing the death penalty in the case. Rather, he says, the government's position now is that it has no position -- pro or con -- on the death-penalty issue.

Previously, government prosecutors had argued along with Larson that the death penalty did not apply to the Whitworth case. They indicated that they would not seek it, citing the 1983 case of James D. Harper who was convicted in San Francisco of selling documents about US Minuteman missile silos to the Polish intelligence service for $250,000. In that case, the Ninth Circuit Court of Appeals determined that the death penalty did not apply.

This position mirrored those taken earlier by other government prosecutors in Baltimore and Norfolk, who argued in the cases of the other three members of the alleged Walker spy ring that the death penalty did not apply. In each of those cases federal judges declined to permit the Washington Legal Foundation to argue its point and the issue was dropped.

In the Whitworth case, however, Judge John P. Vukasin has agreed to permit the Legal Foundation to argue the death-penalty issue. This has put the Justice Department in an uncomfortable position.

Government prosecutors in the trials of the three Walkers have not pressed for the death penalty because they say federal capital-punishment statutes were overturned by the Supreme Court in a landmark 1972 decision. The Justice Department has long held that new capital-punishment statutes must first be passed.

Kamenar and his allies say the 1972 decision doesn't apply to federal espionage cases. He says the necessary laws still exist and the government is giving up potential leverage in its prosecution of Whitworth.

``They need a bargaining chip out there,'' he says. Even if government prosecutors have no intention of carrying out a death sentence, the threat of execution can be used as leverage to persuade Whitworth to disclose the extent of his alleged spying, he says. Such knowledge is necessary, according to intelligence experts, to assess the possible damage done to US national security and to take proper countermeasures to safeguard future US security.

Kamenar says in the absence of such a ``bargaining chip,'' Whitworth will continue to refuse to cooperate with prosecutors. He notes that even on a life sentence, federal convicts may be eligible for parole in 10 years.

Kamenar adds that by pressing for the death penalty the government would send a strong message to potential Soviet spies, ideally detering them from spying.

``I disagree with the Washington Legal Foundation's interpretation [of the 1972 decision],'' says Stephanie Farrior of Amnesty International, which opposes capital punishment. She says it is widely held in the legal community and in Congress that the 1972 decision struck down federal death-penalty statutes. Congressional action is necessary, she says, to reinstate them.