No, he is not. He is referring to the concept of lax natural transformation as described over at the n-lab, and discussed in this MathOverflow question.
He is referring to the fact that parametrically polymorphic functions can be seen as Functors. It is their parametricity which is seen as a lax natural transformation. Basically this is a uniform way to go from any specialization of a parametrically polymorphic function to any other. The reason it is lax is that things don't commute on the nose (i.e. apply + transport is not exactly the same as transport + apply), but they are up to a given 2-cell.