While peace between Egypt and Israel has never seemed closer, renewed fighting in Lebanon poses serious new dangers to the Camp David atmosphere of accord in the Middle East.

President Carter's public appeals last week and Secretary of State Cyrus Vance's consultations at the United Nations underscore deep concern in Washington and other Western capitals over the battles between Syrian troops and Lebanese Christian militias.

In trying to translate that concern into action, however, woulb-be peacemakers face a bewildering - and explosive - tangle of politics, diplomacy, religion, clan loyalty, blood feuds, ethnic rivalry and mean street gunners.

The 3 1/2-year-old civil war in Lebanon is rooted in seemingly irreconcilable disputes among the country's 3 million inhabitants ad in tensions across the Middle East that are reflected in that sunny little battleground.

The main adversaries in current fighting the 30,000 Syrian troops in Lebanon and the top Maronite Christian fighting forces: the militia of Piere Gemayel's Phalange Party and the "Tigers" militia of former president Camille Chamoun's National Liberal Party.

In the background are hints from Israel that it could intervene in Lebanon again if, in Jerusalem's judgment, the Syrians go too far in their attacks on the Christians. Israel has been notably tight-lipped in the latest explosion, however, reflecting the fears that the momentum of Camp David could be slowed or even reversed if Israel and Syria were drawn into a confrontation over Lebanaon now.

Israel has helped arm the Christian militias and has provided their youthful gunmen with training. The aid is aimed at preventing transformation of Lebanon into more "Arabized," pro-Syrian nation that would turn the rocky southern Lebanese hills over-looking Israel's Hula Valley into a new front in the event of another Middle East war.

Tensions mounted rapidly in Lebanon with announcement of the Camp David accords, which on the surface at least seemed to precipitate the new round of fighting.

On the one hand, Christians complained the Camp David framework for the West Bank and Gaza left no room for return of an estimated 400,000 Palestiniasn in Lebanon. The Palestinians, who helped arouse Moslem dissatisfaction and fought alongside Moslems in the original civil war, are in Christian eyes the underlying cause of Lebanon's problems.

On the other hand, some observers said Syrian unhappiness with the accords also helped touch off the weekend explosion because Damascus was eager to raise tensions and prevent the accords from being carried out.

Base on past experience in Lebanon's tortured recent history, the presence of heavily armed Syrian troops on one side of a Beirut street, with equally heavily armed Christian street fighters on the other side, was in itself a formula for clashes that easily could grow into all-out shelling.

Unplanned street clashes that eventually grew into battles had heavy impact on the civil war that broke out in April 1975. At its beginning, the conflict included;

Conservative Maronite Christians, mainly Gemayel's Phalange Party, Chamoun's National Liberals and the mountain warriors of former president Suleiman Franjieh.

Leftist forces, mainly Moslem, under the overall leadership of socialist leader Kamal Jumblatt and including the Nasserite Murabitoon militia along with a several other lesser groups such as Communists and pro-Syrian Baathists - each with its own armed group.

Yasser rafat's Palestinian guerrillas, who provided their Moslem allies with arms, funds and discreet help from officers trained in the use of modern arms, then entered the fray all-out as part of a joint command with Jumblatt's forces.

Syrian soldiers first entered eastern Lebanon along the Syrian border to underline Damascus' insistence that Franjieh and his Maronite allies bow to Moslem demands for a greater share of power in the Christian-dominated Labanese government system.

But Syrian President Hafez Assad, in a dramatic and unforeseen shift, suddenly switched sides in June 1976 and began shelling his former Palestinian allies in the mountains well inside the country. He later explained that Arafat and Jumblatt had rejected his advice that they compromise and had schemed to inflict a decisive defeat on the Christians in order to turn Lebanon into a Moslem-run state with a strong Palestinian role.

By the time Syrian tanks lumbered down the hillsides into Beirut - in November 1976 - Assad's troops had become the backbone of a pan-Arab force that was set up to maintain peace in Lebanon by a pair of rab summit conferences sponsored by Saudi Arabia.

The Syrians firepower far outstripped anything any force then in Lebanon could muster. They had two missions: to stop the street fighting in Beirut and to give some muscle to Preisdent Elias Sarkis' efforts to reimpose state authority in a savaged nation where the rule of the gun had replaced the rule of law.

Assad had the firm, if quiet, backing of the United States for his peacemaking operation. Special U.S. envoy 1. Dean Brown had played a role in lengthy negotiations that led to the selection of Sarkis, a former Lebenese Central Bank governor known as a political neophyte who could be counted on to follow Assad's advice.

Once in control of Beirut, the Syrian troops effortlessly smothered the last sparks of fighting between the Christian militias, and Lebanese Moslem leftists, aided by their Palestinian allies and mentors.

With the capital occupied, most Lebanese of all persuasions began hoping, perhaps unrealistically, the war that had alternately raged and sputtered for 2 years wa at last ended.

But tensions already were building between the Syrians and such Christian leaders as Chamoun, a crusty silver-haired godfather figure unwilling to take advice from the Syrians he regarded for the most part as bumpkins.

As for Sarkis, Chamoun and everyone else in Lebanon knew he had been installed by the Syrians and that his only authority flowed from the Syrian tanks squatting on Beirut street corners.

So when Sarkis ordered Chamoun's Tigers and their Phalange allies to shed their rag-tag uniforms, turn over their arms and stay off the streets, no one listened. Eager to avoid more bloody clashes, the Syrians backed off and agreed to let Sarkis try his hand politically.

It was his failure over almost two years that set the stage for the increasingly violent fighting between Assad's peacekeepers and the Maronite Christian street fighters loosely allied under Chamoun in the Patriotie Front.

Despite repeated attempts, Sarkis has never persuaded the Christian militias to turn over their abundant supplies of M16s, AK47 "Kalashnikov" assault rifles, 50-caliber machine guns, 106 mm recoilless rifles, antiaircraft artillery, 155mm Howitzers and tanks, along with some French-made rockets.