To obtain the subject lubricant capable of providing a processing lubricant and a pressure medium excellent in dispersion stability, non- combustibility and lubricating properties, containing a specific dicarboxylic acid and a base.

This lubricant comprises (A) a dicarboxylic acid obtained by reacting (i) an 18-20C fatty acid or its polycondensate (preferably an 18-20C monohydroxy fatty acid or its polycondensate) with (ii) maleic anhydride and succinic anhydride under heating and (B) a base (e.g. an alkali metal compound or an amine compound). Preferably, the lubricant contains a polycondensate of an 18-20C hydroxy fatty acid. Consequently, an aqueous lubricant requiring a small amount of the lubricant to be added to water, needing no use of a phosphorus- or a halogen-containing extreme-pressure agent, capable of omitting the addition of a surfactant is expected.