Modifying normal calculations in Sprite Diffuse shader

My billboarding sprites using the Sprite Diffuse shader are being lit irregularly by light sources, sometimes turning completely black because the 2d plane is "edge-on" to the light compared to being completely lit when it's facing the light directly.

If I want the sprite to still react to lighting, how would I do it without this effect?

My best guess so far is I'd have to modify the shader code to calculate the sprite's normals similarly to, say, a pill, and then light the sprite itself accordingly.

Is anybody able to point me in the right direction? I don't know anything about programming shaders so dropping keywords and concepts for me to know what to look for would be immensely helpful.