What would a 'change' coalition mean for Israel?
But building a coalition in Israel's notoriously fractured political landscape is no easy task. Here is a look at the issues.
Will an anti-Netanyahu coalition emerge?
Lapid's Yesh Atid ("There Is A Future") party took second place after Netanyahu's Likud party in March legislative elections, Israel's fourth within two years.
After the combative right-wing premier again failed to cobble together a coalition, Lapid was tasked in May with forming a government.
Former TV host Lapid has until just before midnight Wednesday to gather a majority of at least 61 lawmakers in the 120-seat Knesset.
As of Monday morning, Lapid had the support of 57 lawmakers, with his centrist base and members of the left making up 51.
On Sunday he had crucially gained the support of nationalist hardliner Naftali Bennett, whose Yamina ("Rightward") party holds seven seats, although one of its MPs said he would not join the anti-Netanyahu camp.
Lapid, therefore, needs four more backers and is looking for support among Israeli Arab parties, which have yet to announce their plans.
Speaking on Monday, Lapid warned that "many obstacles" remain.
"Maybe that's a good thing because we'll have to overcome them together," Lapid told members of his party.
"That's our first test -- to see if we can find smart compromises in the coming days to achieve the greater goal."
What unites the 'change' alliance?
The coalition would be a fragile grouping of multiple parties with deep ideological differences, united only in their common desire to topple Israel's longest-serving premier.
It would include centrist groups such as Lapid's party and the Blue and White coalition led by former military chief Benny Gantz as well as historically powerful leftists Labor and Meretz.
But Lapid has also rallied supporters on the right, starting with Avigdor Lieberman's Yisrael Beitenu, a staunchly secular nationalist party backed by many immigrants from the former Soviet Union.
It would also include the hawkish New Hope party, comprised of Likud defectors, and now the religious-nationalist Yamina bloc of Bennett, a former leader of Jewish settlers in the occupied West Bank who opposes Palestinian statehood.
The groups are bitterly opposed on a number of issues, including on the place of religion in politics.
But they share "a genuine belief that Netanyahu is a danger to the country," said Jonathan Rynhold, a political science scholar at Bar-Ilan University near Tel Aviv.
Their animosity is driven by the notion that Netanyahu has "put his personal interests ahead of the country," the professor said.
Netanyahu, 71, is on trial for alleged fraud, bribery, and breach of trust, charges he denies.
In order to maintain unity and survive, said Rynhold, a new government would adopt "an agenda which is largely consensual", focusing mainly on less controversial issues in health, education, and transport policy.
How about the peace process?
Israel's political drama comes shortly after the latest deadly military escalation with the Islamist Hamas group that rules the Palestinian enclave of Gaza.
It also follows years during which the Israeli-Palestinian peace process has stalled and Jewish settlements have been expanded in the occupied West Bank under hawkish Netanyahu.
The issue not only angers Palestinians but also sharply divides Israel's political parties. The left supports the creation of a Palestinian state, while groups on the right want to annex the occupied West Bank.
Rynhold said a multi-party "national unity government" shouldn't attempt major moves now to relaunch the peace process -- because of their divergent views, but also for unclear counterparts.
The Palestinian Authority's president, Mahmud Abbas, is seen to lack legitimacy after more than 15 years in power, he said, while Hamas refuses to recognize the Jewish state.
The new alliance would "reach an agreement on the status quo," Rynhold said.
"But they will have to deal with managing the conflict so that there are not outbreaks" of violence as seen earlier this month.
If fighting breaks out again, the parties are likely to stay united during times of military conflict, he said.
"There is an Israeli consensus on the recent Gaza War. There has been an Israeli consensus on every war since 2000," Rynhold said.
"It will get challenged, but they can pull it off."