per vertex lighting:

NdotL0 = dot(N0, L)
NdotL1 = dot(N1, L)
V = NdotL0 + t (NdotL1 - NdotL0)


per pixel lighting:

N = normalize( N0 + t( N1 - N0 ) );
V = dot( N, L );

So it's the renormalization that introduces the "non-linearity" I guess. Because otherwise you could just distribute the dot product into that expression for 'N' and get the same result as in the per-vertex case.

Here are some screen shots from RenderMoneky showing per-vertex nDotL along with per-pixel with and without the renormalization

Per Vertex:

.


Per Pixel w/out normalize



Per Pixel w/normalize