When Israeli Prime Minister Shimon Peres was presenting Israel's terrible economic plight to Secretary of State George Shultz in a preliminary meeting this week, he was comforted with words to the effect that he would "find his best friend" in the White House. Sure enough, the next day Peres emerged smiling from his session with President Reagan saying he had "found . . . a true friend of Israel."

It figured. Peres stands precariously at the head of coalition forces hanging together for fear of hanging separately if urgent economic problems are not addressed. So even more than is usually the case, Peres needed to convey back home his command of American respect and support. For his part, Ronald Reagan naturally cherished the photo opportunity to re-pledge his allegiance to Israel and its American constituency.

So what else is new in the U.S.-Israeli relationship? Israel's self-professed best friends continue to promise whatever it takes to ensure Israel's economic and military strength. The Reagan administration continues to defend past Israeli policies and its own hand on their behalf; it's business as usual.

Yet there was nothing usual about the way Peres laid out the Israeli government's top priorities: economic recovery and withdrawal from Lebanon "as quickly as possible." In private briefings and closed-door official talks, Peres gave a clear sense that, however inconclusive the Israeli election may have been, at least two new considerations will be cranked into U.S.-Israeli relations.

First, the economic problem. Raging inflation, a towering foreign debt and a crippling deficit in the balance of payments, everybody agrees, will impose the need for a crunching austerity program. This will increase unemployment and reduce living standards. The Israelis wanted -- and got -- a promise in principle that the United States would "stand behind the Israeli economy."

But not even the Israelis can be sure what that might add up to. Estimates run as high as $1.5 billion over the next two years on top of the current $2.6 billion a year in economic and arms aid. Any such figures would crack the U.S. foreign aid program wide open.

So next year's consideration of aid to Israel will be no routine matter. Inevitably it will force debate on Israeli policy and how it reinforces U.S. policy efforts to advance the peace process and protect American security interests in the region.

That debate can only be sharpened by a widening divergence in the way Israel and the United States look upon Lebanon -- and Syria. The latest administration line, as put forth publicly on at least two occasions by National Security Adviser Robert McFarlane, is that the real purpose of the Marine presence in Lebanon was "to try and prevent a war between Israel and Syria; so to say that the situation wasn't helped is simply wrong."

Leaving aside the fact that Syria already had -- and lost -- a short war with Israel before the Marines arrived and that the Marines couldn't have stopped a renewal of fighting between those two countries in any case, Peres talks privately about a Syria that the Reagan crowd would scarcely recognize. He seems to see a trustworthy Syria, wary of deep involvement in Lebanon and ready to cut a deal with Israel that would bring the United Nations into an expanded peace-keeping role to replace retreating Israeli forces. He seems to see a Syria as nervous as Israel is about the growing influence of extremist Shiite Moslem forces that are responsive not to the Soviets but to Iran's Ayatollah Khomeini.

Right there lies another gap in U.S. and Israeli perceptions. The Reagan administration would have the U.S. electorate believe that by ushering out the 15,000 PLO fighters in 1982, it achieved, again in McFarlane's words, "a fundamental change in the source of violence in the area.'

Well, swell, the Israelis would say. But they would not count that as something to be too proud of: they sit in southern Lebanon, taking casualties not from the PLO but from the predominant and increasingly violent Shiite Moslem population. One of the big reasons they want to get out is that they fear their continued presence will further radicalize the large Shiite element everywhere in Lebanon.

In short, Israeli and Syrian interests in Lebanon would appear to coincide more closely than Israeli and American interests. Shimon Peres and his influential defense minister, Yitzhak Rabin, have no problem turning around. Not having been party to Israel's Lebanese enterprise, they can write it off as as a lost cause.

But that leaves Ronald Reagan with a difficult case. He must explain his support for an Israeli policy that Israel no lnger supports -- and at a time when Israel is preparing for unprecedented U.S. commitments to the Israeli economy in the interests of not only Israeli but American security.