He is not as relevant as he keeps telling everyone.
There are only four possible outcomes regarding Leiberman:
1. Likud + all the Religious/Chareidi parties get more then 61 seats and form a government without Liberman
2. Lieberman joins with Likud and the all religious/Chareidi parties to form a government
3. Blue and white + the deep left parties + Liberman + the Chareidim form a government
4. Likud and Blue and white form a government in which case either they don't need anyone else or they need another 5-10 seats in which case it is far more likely the chreidim join.
Any other scenario such as blue and white breaking up after the election or labor party joining a likud government would not require Leiberman's help.
Option 1 doesn't seem likely at all, unless by some miracle Lieberman doesn't cross the threshold to enter the Knesset.
Option 2 would require Lieberman to renege on everything, I don't think this is likely.
Option 3 won't happen as long as Lapid is there, and as far as Lieberman joining, see option 2.
Option 4 is the least unlikely of your scenarios, though I find it highly unlikely.
Blue and White breaking up could be a scenario, but they are well aware of that, and are preempting it, so it's not very likely as long as the breakup didn't occur prior to the election. Labor (which is likely to be renamed) might join (haven't seen yet if they pledged anything anti-Netanyahu).
But all you need to do is look at Greece, Belgium or even the UK and find out what political chaos in a parliamentary system means. I find this as the most likely outcome, and have no clue as to how it gets resolved.