realtime reflection and specular with baked texture

So I'm building a scene in maya and rendering it using v-ray inside of Maya. I export the geometry and render out baked textures including lights/shadows, both are easily imported into Unity - geometry as fbx and the textures as jpg which is applied to a unlit material, which means that I now have a beautiful scene without the need of a single light inside unity - so far so good. I would really love to be able to have realtime reflections and specular effects which react to a few lights around the scene but I don't want to illuminate my textures as they already have light and shadow baked into them - what to do? is my approach wrong? any suggestion would be greatly appreciated!

Thanks Jeppe