The lawsuit intends to give "real consequences to those who selectively target Israel and seek to impose an unjust and illegal boycott against the Jewish state", the group said.
The three Israelis were seeking about $13,000 in damages.
Sachs responded to the legal action on her twitter account saying she had found out about it after an Associated Press reporter, based in Jerusalem, contacted her for comment.
"Israel the only "democracy" in the Middle East where New Zealanders get sued for exercising their freedom of speech.....in New Zealand," she tweeted on Wednesday.
Sachs told the Herald she had no further comment regarding the issue and added "I've said all I wanted to say in the open letter".
In the open letter the two urged Lorde to act "in the spirit of progressive New Zealanders who came before you and continue their legacy".
"Israel might seem like a world away from New Zealand but that shouldn't stop us from speaking out and being on the right side of history.
"Please join the artistic boycott of Israel, cancel your Israeli tour dates and make a stand."
The letter said a peformance in Israel sent the wrong message and would be seen as giving support to the policies of the Israeli government.
Lorde announced late last year she was cancelling her planned June 2018 concert in Tel Aviv.
