A composition of matter suitable for use as a lapping composition is provided which has improved lubricity, abrasive suspension and cleanability and which contains an amide of the formula R 1 CON (R 2 0H) (R 3 0H) in an amount of 4% to 20% by weight and an oil in an amount of 65% to 96% by weight. The lapping composition may have a wide range of amounts of water mixed into it to form a water-in-oil emulsion in which an abrasive agent may be suspended. Because of the wide ratios available between the water and oil phase amounts, the emulsion can be prepared relatively oil rich for fine lapping operation and may later be diluted for rough lapping operation.