Look, it's not even clear that the government will survive enough time until he comes to power, one (right-wing) member of the coalition already resigned as it is, leaving the coalition without a clear majority, and Netanyahu is pressuring them for all he's worth. It's not implausible that we'll see an election before Lapid takes over.
Even if he does get his chance, he'll be leading the exact same coalition as right now. Just like the left-wing members are constraining Bennet, the right-wing members are equally going to constrain Lapid. Expect more of the same in general.
Finally, I don't see any party realistically succeeding to negotiate with the Palestinians on anything serious, Lapid or otherwise: they are fragmented, Hamas and Islamic Jihad are as openly genocidal as ever, the supposed "good guy" Abbas is vile and corrupt, the Palestinian street is as hostile to the idea of Israel as ever, and there was a recent wave of brutal terror attacks to boot, which doesn't exactly predispose the Israeli public toward negotiating either.