THE SOLUTIONS commonly proposed to the crisis in Lebanon recall the classic perscription for insomnia: get plenty of sleep. In Lebanon's case, the customary advice is for the outside military forces of Syria and Israel to depart, for the Palestinians to disappear, and for the Moslem and Christian communities to make up and put their country back communities to make up and put their country back together again. But only a cynic can argue that these bromides have any current relevance. The latest surge of violence underlines the point.

Apparently, Christian militias, for purposes they justified as defensive, were strengthening their position around Zahle, 30 miles east of Beirut. Syria, which still has in Lebanon the forces invited in as peacekeepers in 1976, took this as part of an Israeli-backed plot to open up a potential invasion corridor to Damascus, and began shooting. Syrians have killed some hundreds of civilians, and a firm cease-fire is not yet in place.

Secretary of State Haig, who happened to be traveling in the area, promptly denounced "the brutalties of the Syraisns' action against the Christian enclave." It was good to have this unequivocal American reaction, the more so because it was voiced in a part of the world where the killing of Arabs, and especially of Christian Arabs, by Arab guns does not usualy excite much concern. Mr. Haig's remark, too, was consistent with his broader effort to distinguish those Mideast nations that are ready to join the United States in a "strategic consensus" against Soviet expansion from those, such as Soviet-allied Syria, that presumably are not. If the remark was an accurate foretaste of American policy in Lebanon, however -- he later insisted it was not -- it was off base. Syria must be condemned for firing on civilians. But just as Israel has reasons -- essentially, self-defense -- for its military operations in Lebanon, so Syria also has its reasons. Some of these have to do with its traditional contempt for Lebanese sovereignty and its paranoia about Israel. But these reasons also have to do with keeping Christians and Moslems for resuming the battle that produced 40,000 Lebanese dead in 1975-76. To many Mideast ears, Mr. Haig was suggesting that the United States might abandon its traditional policy of support for Lebanon's integrity and of neutrality in its communal strife. To move toward Israel's policy of backing the Christians in a partitioned state would only polarize Lebanon further and draw outside powers more deeply in.

As appealing as is the French proposal, supported by the Americans, for a multinational peace-keeping force to protect the Christians, Syrian hostility makes it a long shot. Not too much can be promised to Lebanon: sad experience indicates that not much can be done there. It is the "Cambodia," the sideshow, of the Arab-Israeli dispute.