Business page, user locked, business page still alive

You need to get the old account unlocked before anything else can happen.

I would suggest also creating a new page and directing your clients there. Not everyone will migrate. Unfortunately, that's life in the big city. With a new page (or if there's any way to wrestle control back of the old one), make a trusted associate a fellow administrator. If it's your business partner (if you have one), then make sure it's clear in the partnership agreement-- which you'll have to amend-- how to handle things if you part ways. Same thing with a spouse if you have a prenup.

I am suggesting written plans in place for if/when circumstances change so you don't get into a situation where an administrator locks you out.

But if my old user will get deleted, does my business page also get terminated?

Pages are independent of their owners.

So it most propably live till the end of the Facebook?

I couldn't possibly know that.