“Lapid can easily persuade the Chareidim by offering the option to leave kollel without joining the IDF and the Chareidim can easily persuade Lapid by offering to accept the same.”
I think the former is true but not the latter.
I disagree. You have to remember what the “real” desire is for both sides. Lapid (contrary to popular belief) does not seem to want every member of Klal Yisroel to be eating ham on Yom Kippur (I know Akuperma & HaKatan will disagree, so consider your posts posted). His power comes from the social protests movement. If he can show that he is no longer paying for Charaidim learning, he will consider that a “win”. Letting Charaidim work without stopping payments for the vast majority (at least to start) who will stay in learning is a “loss”, so why would he agree?
They could add that those who stay in learning lose payment and go Satmar, and that Lapid (IMHO) would agree to. The court issues can be solved as I have posted earlier.