I don't really understand why the Blitz3D lighting won't work with my level, but trust me, it simply refuses to illuminate the geometry.
Lights work on vertices. This measures the amount of light hitting each vertex and interpolates it across the triangle between vertices. So a triangle lit with white light in one corner and no light in the other two will show a gradient of illumination from one point to the opposite edge.
Now imagine you've got a wall, a plain rectangle made of two triangles. If you shine a spotlight into the middle of that wall, the vertices are receiving no light so the light won't show. If instead you use a rectangular mesh of say 20x20 smaller rectangles, the central vertices will be illuminated by the spotlight. However this typs of lighting shows the triangles of the mesh, and you won't get a smooth circular spot. Basically small spotlights are very hard to manage in a vertex lit system. You would need to find another solution like a texturing solution. There's a few examples I've seen including one that projects a bat-signal as though it were a torch light.