Why Israel is holding out in Lebanon

His voice dropping to denote displeasure with the thought, Israeli Defense Minister Ariel Sharon looked earnestly at his audience of American Jews. ''Imagine the situation,'' he said, ''if we withdraw - after everything that has happened - and our northern towns and cities are shelled. What are we going to do? Go again into Lebanon?''

Moments later, matter-of-factly but no less bluntly, Israeli Foreign Minister Yitzhak Shamir told delegates to the Israel Bonds convention: ''We are concerned what will happen the day after our withdrawal. The PLO will try to return. The Lebanese Army is too weak to stop them.''

Enduring security - that is the overriding theme expressed by Israeli government officials as the Israeli-Lebanese-American negotiations on the future of Lebanon continue, deadlocked, into their second month.

Besides the universally agreed upon need for secure borders for Israel, the government's own credibility is at stake. The speeches Jan. 26 by the second and third most important men in the Israeli Cabinet, coming at a time of strained relations with the United States, provide a valuable insight into official Israeli thinking. And they seem to indicate little give in the Israeli position.

The costly, image-tarnishing war in Lebanon was conducted, the Israeli leaders have contended, to drive the Palestine Liberation Organization out of Lebanon once and for all and to achieve the much-promised ''peace for Galilee.'' If the north of Israel is harassed in the future (there have been three incidents of Katayusha rockets being fired, harmlessly, into Galilee from southern Lebanon in the past three weeks), the Menachem Begin government is in trouble. Mr. Sharon, in particular, has been associated with the war in Lebanon as the architect of the invasion.

Mr. Sharon told his audience Israel is holding fast to four basic conditions necessary before the Israelis agree to a settlement. He indicated there is little room for compromise on these conditions since they involve matters of ''life and death'' for Israel:

1. No PLO guerrillas or political operatives may remain in Lebanon, nor may any forces from any country - Arab or otherwise - remain in Lebanon unless that country has relations with Israel. Mr. Sharon estimated there are 8,000 Palestinian guerrillas still in Lebanon and claimed some are ''coming back into the camps in west Beirut'' and operating against Israeli forces ''from behind the lines of the multinational forces.''

2. The PLO must leave first, then Israel and Syria can remove their troops simultaneously.

3. A 30-mile security zone must be established in southern Lebanon, to be patrolled by Maj. Saad Haddad's pro-Israeli militia. The Haddad forces, whether integrated back into the main Lebanese Army or not, would remain in control of southern Lebanon until the Lebanese Army is strong and reliable enough to take over. And, Mr. Sharon candidly added, ''that may take years.''

4. In this zone there must be placed three temporary Israeli outposts, which Mr. Sharon described as ''anti-terrorist supervision stations,'' to give Israel ''very specific information about any attempt by terrorists to reestablish infrastructure in southern Lebanon.''

Mr. Sharon said these outposts could be staffed by less than 750 Israeli soldiers, but they would be necessary until the Lebanese secret police are sufficiently strong to take over ''anti-terrorist'' operations themselves. The posts would ''not need to be equipped with electronic devices'' for cross-border snooping on Syria or Jordan, said Mr. Sharon, since existing Israeli outposts already perform that function adequately. He said neither the United Nations nor the multinational peacekeeping troops, nor the US Marines on their own could do the job Israel needs done.

5. Lebanon and Israel must have peaceful and normal relations, including open borders and open trade. Foreign Minister Shamir stated, ''We must come to a peace treaty between Israel and Lebanon.''

Mr. Sharon said that normalization is necessary so that ''on both sides of the border people will know they have something to lose if they do not stick to this peaceful situation.'' He pointed to the cross-bridge traffic between Israel and Jordan and the close coexistence, across the Jordan River valley, of Israeli and Jordanian farmers as an example of how de-facto normalcy ensures peace.

Each of these points is controversial, particularly those involving Major Haddad and the early-warning stations.

As the US sees it, these reflect on Lebanon's basic right to control activities within its own borders. US officials argue that Israel cannot call the shots inside the Lebanese Army and that if the Israelis have early-warning stations in Lebanon the Syrians can demand the same. Furthermore, the US argues, a peace treaty could cause problems with Lebanon's Arab neighbors.

Sharon and Shamir both cited the differences Israel and the US have on these issues. Both noted that these involved vital Israeli national interests, while to the US they were simply items on a huge global agenda. Mr. Shamir seemed most critical of the American attitude, calling it a contradiction that ''our American friends are stressing the argument for Lebanon's sovereignty and independence but disregard the surrender of Lebanese sovereignty to Arab pressure.''

Both men also rejected the Sept. 1 Reagan plan, which calls for ''self-rule'' for Palestininans of the West Bank and Gaza ''in association with Jordan.''

Mr. Sharon argued that the ability of Palestinian guerrillas to ''give us real problems from among the 270,000 Palestinians in Lebanon'' was an indicator of how difficult it would be to maintain security if the 1.1 million Palestinians in the West Bank and Gaza were not under Israeli control. Mr. Shamir rejected any peace process other than the Camp David autonomy plan.