For newly created objects the origin is placed in the geometrical center. You can change it’s position anywhere in the 3dspace relative to the object from the Tool shelf docked on the left of the 3d window (T) or from the menu brought up by the amazing Shift+Ctrl+Alt+C shortcut: I...
This is obviously not your fault as this is a Blender design issue. But this explains why I originally couldn't locate SimpleLattice for Mesh Edit mode : I was looking for it in theEdit Mode Mesh menu, which I temporarily assigned a shortcut to because I assumed it was the same as th...