How do I find lieutenants?

[orangeglacier]

So I'm currently trying to kill my first lieutenant.  I know which tile of the map he's on, but how do I find the lieutenant within there?  Is he in a building/cave?  Is there a mission entrance somewhere in the dungeon that leads to him?  Because I went through all the surface tiles and didn't find a boss anywhere.

[x4000]

As you go through the surface area, you'll see a purple map node that has a mouseover tooltip explaining that it has an evil outpost on it.  Inside that tile, you'll find just one really tall and scary looking tower, which has the lieutenant in it.

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