For precision metal work, I have a steel plate made for the purpose and it uses a thixotropic grease of the Clover brand. The plate is HEAVY and the base is cast so there's minimal (< .00001") flex. The lapping surface is cross hatched to prevent any buildup of lapping compound which would throw off the process. If the plate is kept at consistent ambient temperature, you can get repeatable flatness to spec.

For razors I use the DGLP on my Shapton glass stones supported flat by the stone holder and in the pond with its specially treated surface (very very flat and no slippage) on top of a granite surface plate flat to .0001" across the whole surface. This setup gets me consistent and repeatable results.