When U.S. Ambassador Samuel W. Lewis left Prime Minister Menachem Begin one day last month after a scathing, 45-minute dressing-down sparked by the Reagan administration's suspension of the U.S.-Israeli strategic cooperation agreement, Lewis turned to an aide and remarked, "I've seen better political theater before, but not to such a small audience."

In fact, since he arrived in Tel Aviv five years ago as former president Jimmy Carter's envoy to Israel, Lewis has stoically sat through an average of one such outburst a year. He is known to regard some as harsher than last month's monologue, in which Begin accused the Reagan administration of treating Israel like a "vassal state" and declared the strategic accord canceled.

As usual, that admonition was prompted by U.S. attempts to forestall "surprises" by the unpredictable and strong-willed Begin. In this case, it was U.S. displeasure over Israel's annexation of Syria's Golan Heights and, in the words of Secretary of State Alexander M. Haig Jr., the desire "not to create an atmosphere in which blank checks are available for the leadership in Israel."

But, as in the past, Begin made clear to Lewis that his wrath was intended for the policy-makers in Washington and not for the bearer of the message. Sources present at the meeting said that Begin prefaced his statement to Lewis with a warm personal greeting and some friendly rumination before turning suddenly to a stenographer and beginning what appeared to one witness to be a "well-rehearsed extemporaneous speech."

The next day, Begin telephoned Lewis on some pretext. During the conversation he underscored that there was nothing personal in the bitter attack on U.S. Middle East policy and that he was merely presenting a position to be conveyed to higher authorities in Washington.

Seemingly endless Israeli rebuffs of U.S. calls for Israeli restraint in dealing with Arab neighbors have included expropriation of occupied Arab land and settlement of more Israeli civilians there, incursions into Lebanon, bombing of an Iraqi nuclear reactor, destruction of a civilian neighborhood in Beirut and annexation of the Golan Heights. These have raised questions in the State Department about whether events beyond Lewis' control have impaired his ability to get across to Begin what the Reagan administration regards as unacceptable Israeli conduct.

At the same time, in the face of continued U.S. pressure on Israel to show more restraint, some Israeli officials have begun to wonder quietly if Lewis has made the U.S. administration conscious of Israeli determination not to be dictated to in matters it considers vital to its security and continued existence.

"Obviously, Lewis isn't getting across to the Reagan people what Begin's visceral feelings are about certain issues, because the United States is still trying to punish us for our positions on those issues," said one of the prime minister's aides. Nevertheless, he promptly added this caveat: "That may not be Lewis' fault. It could be Reagan's own problem. Maybe Washington isn't listening to what Sam is saying."

Another Israeli official said, "Lewis understands Begin, but I don't think Reagan does."

On the face of it, Lewis does appear to understand and appreciate Begin's "visceral feelings," feelings stemming from ingrained insecurity and a need for national identity that go back to the genocide of Nazi Germany and five wars of survival in its aftermath, and also to 3,000 years of Jewish history.

Lewis has had long talks with Begin about the Jewish experience in world history and Begin's own personal tragedies in wartime Poland, in a Soviet prison camp and fighting British troops in Palestine before the modern state of Israel was created.

He has often said that one cannot understand Israel, and he has given Israeli officials the impression of being a serious student of Israeli society, Zionism and the psychological character of this country. He has developed along the way a reputation in Arab capitals of having succumbed to the diplomatic affliction known as "clientitis," or identifying more closely with his host government than with the policy goals of his own government.

Lewis has become immensely popular in Israel, among officials and ordinary Israelis, frequently speaking out in support of the Jewish state and appearing at Israeli public events, donning his now familiar yarmulke (skullcap) if the occasion calls for it. His popularity is in sharp contrast to that of his predecessor, Malcolm Toon, who spent most of his professional career in communist countries and who often rubbed Israeli officials the wrong way with his bluntness.

It is, perhaps, a measure of Lewis' rapport with Israeli officials that not even a whimper of complaint came from the Begin government when a biweekly Washington newsletter recently disclosed a classified cable the ambassador sent to Washington at the end of December, after the Golan annexation, outlining 10 surprise measures Begin might take before Israel's final withdrawal from the Sinai Peninsula on April 25.

As reported by the Middle East Policy Survey, the contingency list included as most likely: transfer of the prime minister's office to East Jerusalem, an Israeli invasion of south Lebanon, an air strike against Syrian missiles in Lebanon's Bekaa Valley and a stepped-up campaign against Palestine Liberation Organization targets outside Lebanon.

Less likely were: not completing the Sinai withdrawal, continuing overflights over Saudi Arabia, extending Israeli law to the West Bank and Gaza Strip, refusing to relinquish control of two small islands in the Tiran Strait and bombing nuclear facilities under construction in Libya and Pakistan.

The list reportedly was solicited by Assistant Secretary of State for Middle Eastern Affairs Nicholas Veliotes and was presented not as predictions, but as possibilities. U.S. Embassy officials refused to comment on the report of the list.

Israeli officials, who normally are not hesitant to react to such reports, treated Lewis with kid gloves, withholding comment. When asked about it at a news conference with Haig here Jan. 15, Israeli Foreign Minister Yitzhak Shamir replied, "I don't know anything about this information, and I think if it was published anywhere, it is not correct." The Middle East Policy Survey report had already appeared in the Israeli press.

Even by diplomatic standards, Lewis is cautious. He rarely talks with reporters about any subject on the record, and he is even less likely to talk openly about his sensitive assessments of the Begin government that are sent to Washington.

But he is known to be deeply concerned about the state of U.S.-Israeli relations and the danger of the strain getting worse after the Sinai withdrawal, if the negotiations on Palestinian autonomy completely break down and U.S. pressure on Israel is increased.

He is also known to be dismayed at Begin's recent precipitous behavior, displayed particularly during the prime minister's convalescence from a broken thigh bone when Israel made its Golan Heights move.

But on a deeper level, Lewis' exasperation stems from what he apparently feels is Begin's inability to come to terms with the Reagan administration's doctrine of parallel military and strategic alliances with both Israel and such moderate Arab states as Saudi Arabia.

Adding to the exasperation is Begin's impression that Israel can continue to take actions that might be against U.S. interests in the region without consulting the United States, but that the Reagan administration should always consult with Jerusalem before it takes actions that may conflict with Israeli interests.

It is that fundamental incongruity, coupled with Begin's fierce independence and pride in self-reliance, that has led to much of the friction between the two normally steadfast allies.

A vehicle for relaxing the tensions, Lewis feels, could be Haig's increased personal involvement in the Middle East. Haig and Begin have known each other since 1973, when former president Richard Nixon visited here. On one occasion, Haig was seated next to Begin at a dinner, four years before Begin became prime minister. The two were said to have had a long private conversation and to have made a strong impression on each other.

Haig, a strong advocate of the strategic alliance concept, and Begin, who pushed the same concept from this end, share an intense wariness of Soviet intentions in the Middle East, and Lewis is understood to have counseled the secretary to try to exploit that commonality.

Whether the secretary can succeed may be known more clearly following his visit here in the past week.