After the new independent group of MPs formed last month, Sir David told the Observer: "I've been asked whether I will financially support the new group. I have already done so."
Lib Dem members complained about the Facebook post, saying it was antisemitic.
A party spokesman told the JC: "The party has suspended the Lib Dem Friends of Palestine organisation pending an investigation."
Meanwhile, Asa Winstanley, an Eletronic Intifada contributor, was suspended by Labour on Thursday, after it emerged he was a party member.
Mr Winstanley called the Jewish Labour Movement an "Israeli embassy proxy" that engaged in "shameless sabotage of the party" by submitting a dossier of Jew-hate in the party to the Equality and Human Rights Commission, which is now investigating.
He even attacked Momentum, the pro-Corbyn campaign group, for acknowledging Labour's antisemitism issue, saying it should rename itself "Momentum Friends of Israel".
