Did I read somewhere that in a case of the Lab, you get all 4 weeks worth of prize support?

Yes, just like with the Base Set. Included in the case is the first 4 weeks of AP support: Big Ring Of Keys & Tire Iron Plot Twists and LE Guardian and Zombie Minions.

The next 3 months worth need to be ordered from WK, as do the LE figures. But they're all available already.

Not in Australia they ain't . The Lab hasn't even come out here yet :'(

But what I ment to ask was, is there four months worth. I mean all four of the prize packs in a case?

No, just the first month - one pack - four weeks. The other three need to be ordered from WK (or Croftminster in your case).