What are the primary tests that are run on lubricating grease?

Being a semi-solid material, lubricating grease has unique properties that are measured with unique tests.  The two key properties are dropping point and consistency.  Dropping point is the temperature at which liquid begins to separate from the grease.  In some cases, the thickener melts, while in other cases liquid separates from the grease without the thickener melting.  In practical applications, this is the temperature at which the grease no longer stays in place.  Dropping point is measured using the laboratory apparatus and technique described in ASTM D2265 (or ISO 2176).  Consistency of lubricating grease is measured by the cone penetration test, ASTM D217 (or ISO 2137).  In that standard test, a cone of fixed dimensions and mass is allowed to drop into a sample of grease in a standard cup; the temperature and time period are defined in the test method.  The test device measures the depth to which the cone penetrates the grease.  That value is used to determine the NLGI consistency number of the grease.