What is the Gauntlet encounter library from?
 

As per the title, I'm wondering what data package I need to purchase in order to see the Gauntlet encounter library. It doesn't seem to be the name of any data package.

That's a single free module, that's not on the "Paizo/Pathfinder modules" list within PF Hero options. It may not be available through HL. Unfortunately, with the current LW store, I can't even look to see if its included in any HL packages without jumping through hoops.
From what I can see, every creature in "The Gauntlet" is in a existing Bestiary. The only exception I note is the half-dragon dire lions, which you can probably recreate in HL anyway.