There is documentation for ArcGIS 9 which states applications will search for a valid license manager in the following order:
1. ARCGIS_LICENSE_FILE (environment variable)
2. LM_LICENSE_FILE (environment variable)
3. LICENSE_SERVER (registry entry)
Does this order of precedence still apply to version 10.3.1. I have tested and it seems that this order is still valid. However I have users that are convinced that the setting in ArcGIS Administrator (LICENSE_SERVER) takes precedence over any other settings.