Forget the orthodox and all the trivial stuff which Lapid is trying to sell as being the most important issue this country faces in modern times ( haredi draft ) and look at the big picture as far as the left is concerned. Bibi rightly doesn't trust Lapid and so doesn't want him in his coalition especially considering that if he and Bennet constantly sided together they would have more power between them than Likud. It would be a government where nothing got done and would be lucky to last a year before the infighting tears the coalition apart. If Shelly is there rather than Lapid & Bennet then Bibi would have some allies in the form of the orthodox which would satisfy him but also Shelly could demand as a condition of joining Bibi address some of the social issues she campaigned on and Bibi would accept. It would mean swallowing her pride and going back on her decision not to join but if she joins the government she can get things done if she doesn't she can proudly sit as leader of the opposition and make speeches and most likely as soon as the parties primaries are held she will be seen as another of the failed leaders who have come and gone in recent years and they will ditch her. Bibi doesn't want Lapid & Bennet the people who voted for Shelly would prefer to see her doing things for them than making speeches so everybody except Lapid & Bennet win. I don't know how iong the coalition will last but probably longer than one where Bibi has to work with Bennet & Lapid and has no allies. If Shelly joins it may even tempt Bennet to break his pact with Lapid and join the coalition and we will then have a more wide ranging coalition leaving just Lapid out in the cold.
Ya'alon okays administrative detention of Jewish extremist suspected in church arson (Haaretz)
from the article: Shelly Yacimovich is the ultra-Orthodox parties’ last hope