Any jolt in any part of the tangled, tenuous complex of regional relations in the Middle East has way of disarranging the whole--in unpredictable ways.

Thus, a carefully constructed American peace initiative for the Middle East now seems likely to go up in the smoke of PLO rockets and Israeli bombs, right at a time when the Reagan administration was beginning to see some hopeful prospects growing out of the futile, brutal and incredibly costly war between Iraq and Iran.

The government of Ayatollah Khomeini had triumphantly thrown back the Iraqi invaders. The conflict remains on an uncertain hold. A resurgent Iran, inflamed by Islamic fundamentalism and reinforced by newly demonstrated military prowess, now looms as a menace, potentially, not only to Iraq but to the Persian Gulf states, to Jordan, by extension to Egypt, the Sudan, Morocco. This, in turn, is said to be giving the so-called "moderate" element in the Arab world some interesting second thoughts about where their security interests now lie.

The Reagan administration had high hopes and elaborate plans for exploiting the perceived result: a general loosening of hard-and-fast Arab positions on the central issue of Palestine. The disruption of these well laid plans as a consequence of the Lebanese shootout could be enormous--the more so when you consider the administration's reading of what had been going on.

The loosening was coming in stages and in various forms, beginning with (1) tangible Arab expressions of concern with the Iranian threat and (2) a widening recognition of the premium imposed on dealing with the sources of Arab-Israeli conflict--on the West Bank and Gaza, the Golan Heights and in Lebanon.

Secretary of State Alexander Haig made this connection more explicit than ever in his recent Chicago speech on the main elements of U.S. policy for the Middle East. He spoke of regional security, but not in the old simplistic sense of a "strategic consensus" against the Soviets. Rather he dwelt on three issues: the Iraq-Iranian war; the Camp David process aiming at "full autonomy" for the West Bank and Gaza; and the turmoil in tormented Lebanon.

"Each of these issues is characterized by a mixture of danger and opportunity," he declared. "Moreover, they have begun to affect each other. If we are to succeed in advancing our goals throughout the region, then we must coordinate our approaches to all of them."

"Coordination" was under way, and intricate. Special U.S. envoy Philip Habib, architect of the now shattered cease-fire across the Lebanese/Israeli border, was headed back to work on the awesome chore of restoring strong central government and territorial integrity to a Lebanon torn by factional strife and semi-occupied by Syrian "peace-keepers" and a heavy PLO military force. Instead he had to devote his energies to restoring store the cease-fire between Israel and the PLO.

Another special envoy, Richard Fairbanks, who is handling "autonomy," was to be off for Europe to rally support for a full-court press on the Camp David formula. In advance of Israeli Prime Minister Menachem Begin's visit here later this month, a big effort was to be made to remove a senseless symbolic stumbling block: Israel's sudden insistence, after more than a dozen "autonomy" talks in other locations, that the Israeli, American and Egyptian "autonomy" negotiators be willing to meet in Jerusalem.

If Reagan and Begin could resolve this issue (a choke-point for Egypt) then Egyptian President Hosni Mubarak would follow Begin to the White House by way of giving the "autonomy" effort a high-powered push.

Meantime, in the Gulf, the United States is expressing its own anxieties over Iran with contingency plans for a heavier American military presence--including naval deployments and even the stationing of aircraft and prepositioning of supplies in Saudi Arabia. And the Americans are finding the Saudi Arabians, with a nervous eye on Iran, more amenable than in the past.

Jordan, too, is alarmed by the weakness of its ally, Iraq, and by the alliance of its traditional enemy, Syria, with Iran. There are indications, accordingly, of subtle softening in King Hussein's adamant anti-Camp David stance. For its part, Egypt has been offering honest brokerage of the autonomy issue from its unique position: the largest of the Arab states, at peace with Israel. Egypt's return to an Arab leadership role could well be advanced by its inclusion in a meeting of Arab "moderates" called by the Sudan. The subject: how to make peace between Iraq and Iran.

"There are various lights flashing," said one European diplomat--before the Israeli invasion of Lebanon threatened to snuff out every glimmering of hope.