Scientists at the Lawrence Livermore nuclear weapons laboratory in California have designed yet another neutron weapon that could turn into the most controversial so far, an artillery shell for the relatively commonplace 155-millimeter gun. But the Pentagon is having second thoughts about producing it, according to informed sources.

The shell is so small, roughly six inches in diameter and three feet long, that for several years it was considered doubtful that scientists at the laboratory could make it into a neutron device, meaning into a very low-yield hydrogen bomb whose radiation output travels farther than its blast and heat effects.

Two other neutron weapons are already in production, the Lance missile warhead and an eight-inch artillery shell that is about one-third larger in size than the 155 mm. Just these have created enormous controversy in Europe; critics fear lower-yield nuclear weapons would make it easier for governments to start nuclear wars.

There are far more 155-mm. guns in Europe in the hands of U.S. and North Atlantic Treaty Organization troops than eight-inch howitzers and Lance missiles.

The new shells would be costly; they would run nearly $1 million apiece, according to congressional sources. And because of their relatively short range--up to 18 miles with a rocket booster--they would plainly be intended for use on Western European soil, which is sure to make them even more controversial among the growing peace movements in Europe.

The Reagan administration last March told the Department of Energy to move ahead with production of the 155-mm. shell, but officials yesterday said a new Pentagon study has now been ordered as to whether the Army needs a second neutron artillery shell, given the controversy in Europe that accompanied the decision last August to produce the larger eight-inch variant.

During a recent series of interviews with NATO officials in Bonn, London, Rome and The Hague, the point was regularly made that any new discussion of controversial neutron weapons for Europe could endanger the politically fragile alliance decision to put new U.S. cruise and Pershing II missiles in Europe.

Because of the controversy over the neutron Lance and eight-inch artillery shells, Defense Secretary Caspar W. Weinberger ordered that they be stockpiled in the United States, and deployed to Europe only after consultations with the allies on whose soil they would be placed.

A Pentagon official said yesterday that the 155-mm. shell production decision might be postponed "into the long-term future."

A White House official said Livermore had proven it had "the capability" to produce the smaller neutron shell, but that the production "threshold had yet to be crossed."

Congress has already expressed its doubts about the need for a second new neutron artillery shell.

In an appropriations bill signed by President Reagan last Friday, Congress cut back on fiscal 1982 money that the administration wanted to start production of the 155-mm. shell. Instead of the $35 million the president asked for, Congress approved $15 million, not enough to begin the program, according to sources on Capitol Hill.

Led by the conservative House Armed Services Committee, Congress has for several years questioned how far the United States needs to go in modernizing its nuclear shells. Roughly 2,000 U.S. 155-mm. and eight-inch nuclear artillery shells, some of them 20 years old, make up a good portion of the 6,000-warhead stockpile now maintained in Europe for American and NATO troops.

If a new neutron 155-mm. shell is not produced, questions will be raised about the future of the more than 1,000 older 155-mm. shells now in Europe. They can fire about nine miles, have yields of less than a kiloton (equal to 1,000 tons of TNT) and do not have the modern safety devices that permit them to be rendered inoperable if stolen by terrorists.

Congress, in its nuclear weapons appropriations bill, also cut back on funds for two other warheads, the ground-launched cruise missile and the new MX intercontinental ballistic missile.

The cruise missile reduction of $15 million was in operating rather than production funds. The funds that were held back can be obligated by the administration once it has shown the Appropriations committees that the new warhead for the cruise missile has been successfully tested and production facilities exist to begin turning the warhead out.

An administration official said yesterday he did not think the congressional limitations would have any effect on the now-planned December, 1983, initial European deployment date for the missile.

The Congress cut almost $50 million in fiscal 1982 production funds for the MX warhead. That reduction, according to congressional sources, could prevent new design work on an MX warhead, although the Carter administration had already chosen the existing Mark 12A warhead for the first MX missiles.

An official of the Department of Energy said yesterday that he didn't know how the reductions in the bill would be divided up, but added that some reprogrammings would be done to make certain "production facilities existed to meet the planned initial operational dates of the missiles."