Swept by national euphoria reminiscent of the first heady days of peace with Egypt, Israel is plunging headlong toward what it hopes will be normalized relations with Lebanon even as its Army tightens its occupation there.

Anticipating a peace treaty with Lebanon once the Palestine Liberation Organization and the Syrian Army leave the beleaguered country -- and after the Israeli invasion force departs -- the Israeli government is planning to accelerate a flourishing commerce and industry exchange that already has begun in the Israeli-occupied part of the country across what amounts to an open border.

The last word is not in yet from the Lebanese government, and probably will not be until elections are held for a new government and life assumes some semblance of normality. But the Israeli government is already counting on Lebanon becoming a major trading and tourism partner.

In fact, trade with Lebanon last month topped $4 million, which is four times the monthly imports Israel receives from Egypt, exclusive of the oil it purchases from the Alma oil fields it returned to Egypt along with the Sinai Peninsula.

Lebanon soon could rank alongside the 10 European Community nations with which Israel conducts most of its trade, in the view of David Brodet, director of Lebanese commerce for the Israeli Ministry of Industry and Trade.

"They are anxious. They are very sharp businessmen and natural traders. I see a large potential for trade between Israel and Lebanon," Brodet said in an interview. He predicted that the $4 million monthly trade rate can be doubled in the first year, followed by a period of steady growth.

When asked whether Israel is not falling into a trap similar to the euphoria that followed the Egyptian peace treaty, which was followed in turn by deep disappointment over Egypt's reluctance to engage in anything more than token trade and tourism, an aide to Prime Minister Menachem Begin said he saw a major difference between Lebanon and Egypt.

Lebanon does not have an extensive state-owned industry as Egypt does, he said, and therefore will be more amenable to opening up trade.

"They also are more free-spirited and much less used to government regimentation," the aide said. "They have fewer problems with fraternization with former invaders than the Egyptians, who always had one eye on the rest of the Arab world. Besides, Israel and Lebanon are closer together than Egypt and Israel, and it will be nothing to go back and forth."

So far, Israel has not imported any goods from war-shattered Lebanon, but it has exported food, textiles, plastic goods and building materials. In the future, Brodet said, Israel can expect to export high-technology products such as medical diagnostic equipment and other specialized electronics.

The ministry has opened an office in the occupied port city of Sidon, where, officials said, an information office has been swamped with inquiries by Lebanese manufacturers and exporters, both Christian and Moslem. Brodet said Israel has no dealings with the Lebanese government on trade, and that business so far has been conducted informally on an exporter-to-importer basis.

There are other symptoms of the kind of peace fever that gripped Israel immediately after the signing of the Egyptian-Israeli peace treaty on March 26, 1979.

Bright red buses from the Egged Cooperative of Tel Aviv regularly ply the coastal highway from the Israeli border through southern Lebanon to East Beirut, filled with tourists eager for a glimpse of a neighboring country that they have long associated with terrorism and cross-border guerrilla raids on Jewish settlements.

Most of the visitors are semiofficial guests of the Israeli state, representing such groups as the United Jewish Appeal or Israel Bonds, but Israeli travel agencies already have begun planning package tours of Beirut for ordinary tourists from Israel and abroad.

The Israelis are also encouraging tourism from Lebanon to Israel, and hundreds of Lebanese already have booked trips to Tel Aviv. Galilee Tours intends to operate two four-day trips a week from Lebanon to Israel to start, and expand the service later.

Last week, 14 Lebanese tourists from East Beirut and other former PLO strongholds such as Sidon, Tyre and Nabatiyah crossed into Israel for a four-day trip, the first such package tour. Organized by a Sidon travel agent, the tour group visited Moslem and Christian holy sites in Jerusalem and the Galilee.

Yesterday, a soccer team from Marjuyun played an Israeli team in Rehovot, south of Tel Aviv, to a 1-1 tie as part of a two-day visit to Israel by 38 residents of southern Lebanon.

An Israeli air charter company has opened regular service between Tel Aviv and an airstrip near Nabatiyah, and El Al, Israel's national airline, has opened a branch office in Sidon.

The El Al office, located amid stacks of ammunition crates on the floor below the Israeli Army regional headquarters in a local government building, sells tickets to Lebanese for travel to other countries by way of Ben-Gurion Airport near Tel Aviv, and arranges bus transportation and overnight stays in a Tel Aviv hotel.

"It took years to get Egyptian tourists to come to Israel, and still it is only a handful of them. This could develop into a substantial tourism industry," the prime minister's aide said.

Ezer Weizman, the former defense minister, used to like to reminisce about his youth in Palestine before Israel was established in 1948. In conversations, he has often recalled crowding into the family car with his father and uncle and other relatives on Saturday mornings and driving up to Beirut to escape the heat and to have lunch by the sea along the fashionable Corniche Mazraa.

Israelis often talk fondly of those days, envying the coolness of Lake Qirawn, the mountains north of Beirut or the hills around Jazzin. They also are attracted by a vision of gambling casinos, nightclubs and excellent French restaurants in Beirut -- the "Paris of the Middle East."

In exchange, Israeli travel agents say, Israel can offer Lebanese visitors the bustle of Tel Aviv and the enchanting serenity of Jerusalem. Christian Lebanese can look forward to pilgrimages to holy sites in Bethlehem, Nazareth, the Galilee and Jerusalem.

The ultimate goal for Israel is a formal treaty of peace with Lebanon, which for years before the Lebanese civil war Israelis used to like to say would be the first Arab country to make peace with the Jewish state.

Begin has said that any solution to the Palestinian guerrilla and Syrian Army presence in Lebanon must be followed by a peace treaty between the two countries.

A Foreign Ministry official said today that the prime minister meant that a peace treaty is inevitable.

"We believe that once all foreign forces are out of Lebanon and an independent government is elected, the government would want to have a peace treaty with us. There is no reason for it not to," he said