The main problem with this segmentation is that it is created from a volume that has spacing between slices that is about 10x larger than pixel spacing within a slice. Use Crop Volume module to resample the volume with isotropic voxel size by checking Isotropic spacing checkbox and selecting B-spline interpolation. It is also advisable to set the region of interest to be just slightly larger than your region of interest (crop the rest of the volume to reduce memory need and processing time during segmentation).
After this, segment the lungs again. It seems that contrast between lungs and surrounding structures are quite good, so you may can segment very quickly and accurately using Grow from seeds effect or Watershed effect (to get Watershed effect, install SegmentEditorExtraEffects extension).
Difference between LM and GS volume is that GS only considers that region that is included in both the segment and the selected grayscale volume node. Usually the grayscale volume contains the whole segment and so the LM and GS volumes are the same.