Right and Left don’t really mean the same things in Israeli politics. Netanyahu’s coalition is a complete mess. He’s allied himself with all of the religious parties, most of whom are socialist leaning welfare statists and a centrist party that wants more government intervention in the national economy. He’s lost Avigdor Lieberman in the negotiation process, which means he’s ruling by one vote. He’s going to be herding cats from day one to get even the most basic functions of government to move along. If Lieberman stays out of the coalition, they’ll be having new elections within a year.
You have two right/left splits: the national defense hawks vs. doves, and the religious vs. secular split. And many people are "right" on national defense but "left" on religious issues. Lieberman's Yisrael Beteinu party is hard-right on defense issues, but represents mostly non-religious Jews from the former USSR.
He’s lost Avigdor Lieberman in the negotiation process, which means he’s ruling by one vote.
I read that Lieberman stayed out precisely because of the concessions Bibi made to United Torah Judaism (one of the two religious parties).