Yair Lapid's Yesh Atid Party, which garnered a critical 19 seats in this recent Israeli election, did not actively campaign on the issue of the peace process, as much as on other domestic issues such as housing for the middle class.However,there is certainly reason to believe that the core outlook of Lapid's party is much more to the left, than the right, and that ultimately, if Yesh Atid is a central part of Netanyahu's new ruling co-alition, voters who voted for Lapid thinking he was centre-right may be in for  quite a surprise.
 
One of the problems with the way the Israeli media reported on the election was that it really did not scrutinize Lapid's platform re Jerusalem by comparing it to his previous pre-campaign positions.There is good  reason to believe that Lapid will in fact be ready to divide Jerusalem, notwithstanding what was his current election platform.
 
Here is what  Lapid said in the election campaign:
 
"Jerusalem is the eternal capital of Israel and its unity is a national symbol of the first degree. Jerusalem will remain united under Israeli sovereignty, for Jerusalem is not just a place or a city but the centre of the Jewish-Israel ethos and the holy place to which the Jews have turned their eyes throughout the generations."
 
However, in May 8, 2008 Lapid gave a very different statement as pointed out by Ha'aretz Barack Ravid on Jan 28, 2013 in an article "Will Lapid divide Jerusalem?" [Notice that the article comes out a week after the election when it really ought to have come out in my opinion, before the election]: "In an interview to Germany's Der Speigel  from May 2008, Yair Lapid unequivocally supported the division of Jerusalem and fiercely attached the Jewish West Bank settlers whose votes he courted in his recent election campaign."
 
In that interview Lapid asserted that "everyone knows how [the Israeli-Palestinian conflict] will end," and forecast with approval that "the Palestinian flag will fly on public buildings in east Jerusalem."
 
Moreover,  Rabbi Shai Piron,  who is second on Yesh Atid's list, genuinely believes in a two state solution and appears ready to divide Jerusalem, and the number three on the list, is a former Mayor of Herzlia, Yael German, who has been previously affiliated with the left of centre Meretz party. She is clearly willing to divide Jerusalem, as is number five on the Yesh Atid list, former director of the Shin Bet Yaacov Peri.
 
In other words, it seems to me that the most reasonable view of the Yesh Atid list is that notwithstanding Lapid’s platform to not divide Jerusalem, his party will in fact be willing to do so if and when the time comes.
 
As such, if Lapid is a major anchor of Netanyahu's coalition, I would expect to see the United States and the international community put real pressure on the new Israeli government to freeze settlements, including East Jerusalem, and to negotiate a two state solution with PM Mahmoud Abbas [That doesn't mean the Palestinians will capitalize on the opportunity, but it does mean that the expectations of the US and the international community for the Israeli government to take steps to renew negotiations and put forward positions compatible with a two state scenario will be real and tangible.]
 
As to Netanyahu's real positions vis a vis a two state solution, I am not that sure. I have tended to believe that up to now Netanyahu has paid lip service to the two state solution, and no more.  And Netanyahu is the more moderate of the Likud members, who are in general to the left of him.
 
But I refer readers to a recent Jerusalem Post piece where Yossi Beilin, an architect of the Oslo Accords and former deputy foreign minister, says that "While not ready to sign a comprehensive peace deal, Prime Minister Binyamin Netanyahu is willing to establish an interim Palestinian state without a final agreement." http://www.jpost.com/DiplomacyAndPolitics/Article.aspx?id=301351. The article is worth a read.

postscript: Here's what Yair Lapid said  has just said reported Feb 5, 2013: Yair Lapid told aides that his Yesh Atid party could opt to stay in opposition and battle Prime Minister Benjamin Netanyahu’s anticipated budget cuts. If so, “in a year-and-a-half, I’ll replace him as prime minister,” Channel 2 quoted Lapid as saying Sunday. He may not be that off the mark, which is why, if you see Lapid stay in opposition, you'll know why.