Note: When dealing with digital structural data, azimuthal bearing is the convention of choice. If you are used to quadrantal bearing, slowly re-familiarize yourself with the azimuth concept, as it is much simpler to encode.
Software used: ArcMap 10.4
0. Make sure your files use a UTM projection.
1. Open the attribute table of your lineament shapefile.
2. Add fields for the starting x and y coordinates, ending x and y coordinates. I used a Double filetype. Calculate these by right-clicking the field heading and select Calculate Geometry...