As the administration struggles to resolve the Lebanon crisis, it also is grappling with another issue that could be even more crucial to the longterm success of President Reagan's foreign policy.

That is the administration's approach to crisis management and decision-making in the wake of former secretary of state Alexander M. Haig Jr.'s excommunication from his self-appointed role as the president's foreign policy "vicar."

In the battle for Beirut--its first post-Haig foreign policy crisis--the administration finds itself in a position similar to that of a baseball team forced to change managers and drastically reshuffle its lineup in the midst of a fiercely contested pennant race.

At stake is whether the United States can achieve the withdrawal of the Palestine Liberation Organization from Lebanon without massive further bloodshed, and then turn the results to America's advantage as a springboard for initiatives to end the Arab-Israeli conflict.

Whether the administration will succeed is still a wide-open question. But the way the strategy has been mapped and pursued represents a great departure from how things usually were done under Haig.

For one thing, except for Reagan, all the key figures in the policymaking machinery have been almost invisible during the tense days of the past week. That's in marked contrast to past crises where Haig--whether making chin-jutting statements to the TV cameras, charging off on shuttle missions or engaging in noisy battles with other officials--somehow always managed to be the man in the limelight.

It has been possible of late to read lengthy newspaper accounts about U.S. policy on Lebanon without finding mention of Haig's successor, Secretary of State George P. Shultz. He has hugged the background so hard that even within the State Department many middle-level officials have taken to calling him "the phantom" and making jokes about whether "there really is a George Shultz."

Officials involved in dealing with Lebanon insist it would be wrong to interpret that as a sign that Shultz is on the sidelines. Instead, these officials say, it means that a collegial approach to decision-making, which the president regards as the most congenial way of doing business, finally seems to be taking root in the foreign policy area.

Lebanon has become a test of Shultz' diplomatic skills and operating style, his relationship with such other powerful figures as national security affairs adviser William P. Clark and Defense Secretary Caspar W. Weinberger and, ultimately, his influence with the president.

Officials say U.S. responses to the situation since last week's outbreak of heavy fighting in Beirut have been developed in discussions involving Shultz, Clark and Weinberger, with occasional participation by White House chief of staff James A. Baker III and Vice President Bush, the nominal head of the crisis coordinating machinery.

Theoretically, that is the way things were supposed to have worked since the first days of the Reagan administration. But in the past, the White House's instinct for a collective approach frequently collided with Haig's inability to adjust to the system. As a result, the system frequently was strained by his threats to resign or to pound the table with Wagnerian warnings about how the future of the free world depended on the decision going his way.

This time around, sources familiar with the process say, the difference can be summed up by one word: Shultz.

Shultz, who served in several high posts during the Nixon administration, has been regarded as a master at working within a collegial system and using it to make his points through reason, persuasion and willingness to compromise.

One administration source describes the difference by recalling an incident at Shultz' first Cabinet meeting. The discussion turned to who should be chairman of an interagency group to deal with foreign trade problems, and Shultz announced that he had just lost his first bureaucratic battle as secretary of state. After weighing the matter, he said, he had recommended to the president that the treasury secretary should head the group.

As the source noted, the contrast with Haig, who became legendary as one of the most compulsive turf defenders in modern bureaucratic history, could not have been more startling.

But, according to the sources, it is in the past few days that Shultz's ability to assert himself in a quiet, but self-confident manner has become most evident. In the period between Haig's resignation and Shultz' getting into office, the sources say a vacuum had developed in the foreign policy area that had been filled largely by Clark.

But Shultz was in his office well before dawn Wednesday after the heavy Israeli shelling of West Beirut began Tuesday night. Since then, the sources said, the lead role in formulating and executing policy on Lebanon has clearly moved back to the State Department.

In coming up with policy ideas, Shultz has worked closely with Reagan's special envoy in Lebanon, Philip C. Habib, and with a group of department professionals including Lawrence S. Eagleburger, undersecretary for political affairs; Nicholas Veliotes, assistant secretary for Mideast affairs, and Sam Lewis, the U.S. ambassador to Israel.

One source describes the process this way: "They, and the people under them, come up with the ideas and option papers. Then it all goes over to the White House where Shultz and Clark and the others kick it around and rework things until there's a consensus on what to recommend to the president."

That, the sources said, was the way in which the administration devised its tactic of having Reagan seek Israeli restraint by maintaining a relatively evenhanded stance in public while privately sending a tough letter to Israeli Prime Minister Menachem Begin. The first draft of the letter was prepared by the State Department, and then it was reworked and modified during extensive discussions at the White House.

Through it all, the sources agreed, Shultz has approached each decision in analytically cool and evenhanded terms. That also is considered to have been an important factor in his dealing effectively with the others during the current crisis, because Haig was generally considered at the White House and the Pentagon as having an overly protective attitude toward Israel.

"By contrast," one source said, "Shultz has acted throughout as neither an advocate nor an opponent. Instead, he has been inclined to listen to every opinion and consider any idea and then make a judgment on what appears to be the pragmatic grounds of what seems best able to meet the problem of the moment."