Paltchik, 24, beat Daniel Eich in the repechages of the under-100kg class to win a bronze medal to follow the medal of the same colour he won at the Tokyo Olympics three years ago.
Lanir, 24, lost to Italian Alice Bellandi in the under-78kg final to close the day's judo.
The pair received loud support from a large contingent bearing Star of David flags but they also heard a few boos and scattered whistling.
In the men's final Zelym Kotsoiev of Azerbaijan defeated Ilia Sulamanidze of Spain.
Israel's participation at the Paris Olympics was strongly opposed by the Palestinian delegation, which argued the Israelis should be barred while their offensive in Gaza continues.
Paltchik has been a hot topic on social media after confronting protestors in Japan and allegedly signing Israeli bombs.
The son of his coach Shay Oren Smadja was killed in the war just days ago.
"I'm so proud. I'm so happy. I'm so thrilled to bring it home, after all the difficult days I've been through," Paltchik said.
"I think it gave me motivation and spirit because the world's going through hell and my country especially," he added.
Paltchik had a nervous moment when the official miscounted his yellow cards and disqualified him with six seconds left of his medal bout against Daniel Eich of Switzerland. After a tense delay, the Israeli was given victory.
Paltchik's coach Shay Oren Smadja, a 1992 Olympic bronze medallist, said it was essential for him to be in Paris despite his son's death.
"I lost my son a few days ago. In the war," he said. "It was very important for me to be here, to bring the spirit. Because we work every day, for years for that moment.
"I asked my wife and my children if it's okay for them that I will be here and they said yes, you can go."
Smadja's son Orem was a 25-year-old soldier in the Israeli Defence Force.
"We love our country and we want to win! We want to win the war."
