THE NEW Israeli government headed by Shimon Peres is showing a welcome burst of energy in respect to Lebanon, where, more than two years after an invasion that was supposed to be a quick in and out, Israeli troops remain, taking casualties sometimes on a daily basis. The new prospect is a result of the Labor Party's decade-long readiness to make certain limited but valuable practical security arrangements with Syria, which calls the important shots in Lebanon today. With plenty of other cares, Damascus, meanwhile, seems to understand it cannot see the Israelis out, and thereby assert the dominant Lebanese role it claims, and reduce the off chance of an Israeli-Syrian collision, without accommodating Israel's border security needs.

Secretary of State Shultz, badly burned last year when Syria tore up the Israeli-Lebanese withdrawal accord he had personally sponsored, is wary of committing Washington -- in a presumed second Reagan term -- to another Lebanese negotiation without suitable guarantees from the parties. It is possible, however, that an indirect Israeli-Syrian-Lebanese negotiation will get started with the help of the United States -- and also of the United Nations, which gets into the play because it disposes of thousands of essential peace-keeping forces in southern Lebanon.

The stickiest issue is the familiar one of the situation Israel leaves behind. Israelis are prone to warn that an early departure could trigger communal violence. The danger is real, but dealing with it is necessarily the responsibility of the Lebanese or -- more to the point -- the Syrians, who have the power. By overstaying the initial welcome they received for freeing southern Lebanon from the PLO, the Israelis have generated fierce resistance from the region's majority Shiites, who nonetheless constitute a natural barrier and the best available one to the PLO's return to the border zone.

Surprisingly, some Israelis still think their security hinges on running a client "South Lebanon Army," manipulating the local groups and otherwise trying to cream off the benefits of a military occupation without suffering its burdens. Experience should have shown that the better bet is to get out of the Shiites' way and, at the same time, to let the United Nations men do their job.

At some point, another go at the West Bank will have to be made. To take up that project too soon, however, would be a powerful distraction, one keeping the Syrians and Israelis from doing what they can and must, in their respective fashions, to help settle poor Lebanon down.