Secretary of State George Shultz sat at the round dinner table between Israeli Foreign Minister Yitzhak Shamir and Defense Minister Moshe Arens last night at the Israeli ambassador's residence. Suddenly all the lights went out except for the votive candles on the table. Security people went on red alert. The Israeli television cameramen denied their lights had overloaded the circuit.

Finally, the new Israeli ambassador, Meir Rosenne, a man with an international reputation as a wit, explained, "You see we need economic assistance . . . I couldn't pay the electric bill."

It was Rosenne's first dinner party since his arrival and was held amid U.S.-Israeli talks on Lebanon. The approximately 75 guests included such American Jewish leaders as Alleck Resnick, president of the Zionist organization of the United States of America, and Dave Brody, director of the Anti-Defamation League, as well as Interior Secretary James G. Watt, attorney Leonard Garment, Sen. Henry M. Jackson (D-Wash.) and Deputy Secretary of State Kenneth Dam.

The evening was full of good feelings, toasts as warm as the weather, and an atmosphere of careful optimism. Shultz said during the after-dinner toast that he thought yesterday's marathon sessions at the State Department had resulted in some agreement on Lebanon that would be good for Israel and for the United States.

Now, he said, "We need to implement the spirit as well as the letter." He added, "I have never been treated so graciously or challenged so effectively. We get along very well, not only the two key ministers who are here tonight, but my new friend the prime minister." He then offered a toast to Israeli Prime Minister Menachem Begin.

Shamir thanked Shultz for his "great efforts to share our view. Thanks to these efforts, we have succeeded in reaching some common goals." Arens said he thought that "we are viewing things the same way."

The defense minister, who was ambassador here until March, added, "When I came to the United States as ambassador a year ago, some people said, 'Well, at least things can't get worse between the United States and Israel.' But they didn't get better, until I left the job."

Israeli Prime Minister Begin had turned down, for "personal reasons," President Regan's recent invitation to come to the United States, and the consensus among those attending the party last night seemed to be that he is in good health but very depressed about the death of his wife, Aliza, last November and the death in June of his deputy prime minister.

The U.S. ambassador to Israel, Sam Lewis, said, "The prime minister's health is about the same as it has been, neither better nor worse. But it was not psychologically the time for him to come. He's still in mourning for his wife. They were the closest couple I ever knew."

Meir Shitrit, at 32 the youngest member of the Israeli Knesset, said Begin is "functioning well. But he has been very depressed."

Former Supreme Court justice Arthur Goldberg added that he has had several letters from Begin. "His health is good but he is despondent after the death of his wife, as anybody would be after a marriage of 40 years when they were so close. I can understand how he feels. Dorothy and I celebrated our 52nd anniversary July 18."

As for the Arens-Shamir visit, Robbie Sabel, the embassy's political counselor, said, "You know, these meetings are so valuable because it's not like cables where you have to wait so long to get answers. You can try out ideas on each other even during the coffee breaks."