DirectionalLight is a directional light… with no fall off and no limited cone or anything. Spot light and point light may or may not light some vertex for various reasons that have nothing to do with its normal.
It works correctly with a directional light. Imfortunately as you said there is no fall off. So if i want to use point light and spot light will i have to create a custom material ?
The problem will be the same. I guess your single triangle is huge when compared to the light fall-off… thus one corner it bright and the other completely in shadow or whatever. General solution is to subdivide the triangles.