Surface Lasso Mode was one of the first tools in Meshmixer, going back to version 1.0. It is an alternative to Brush selection mode that will allow you to select surface regions without having to do a large amount of painting.
Enable Surface Lasso mode using the Brush/Lasso toggle at the top of the Select tool panel. In Lasso mode, make a selection by drawing one or more curves on the surface of the object. To draw multiple curves, chain them end-to-start so that each curve begins very close to the end point of the previous curve. You can change the viewpoint by moving the camera between drawing curve segments. To complete the selection, simply close the loop, ending the final segment near the starting point of the first segment.
Once you close the loop, the faces inside the loop are selected, as shown in the image above. Note that "inside" is defined as the side with fewer triangles, so if you get the wrong side, try the Invert (i) or Invert Connected (shift-i) hotkeys to switch sides. Once the selection is made, you will enter Brush mode and can paint to edit the selection. It is not possible to make multiple Surface Lasso selections.
Note that Surface Lasso can fail in some cases, particularly on meshes with large or very skinny triangles. It will help to draw slowly.