These days it's common to only bake the indirect contribution from analytical light sources. This way you can handle the direct lighting with standard deferred or forward rendering, and apply dynamic shadows using shadow maps or the technique of your choice. In our engine we expose settings on our lights that let the lighting artist choose whether to only bake indirect lighting, or bake indirect + direct. For some cases (for instance, where the light only touches static background geometry) they will completely bake the light so that there's no runtime cost. But for most lights in the foreground they will only bake indirect, and the engine will compute dynamic shadows and diffuse + specular per-pixel.
We also bake shadows for some lights, but we store that in a separate texture. We'll usually use these for areas that are further away from the camera to save on performance.
In terms of energy conservation and making sure that your baked lighting combines properly with other light sources, just take the time to think about exactly what you're storing in the light map and make sure you're not "doubling up" on anything. So if you're just storing indirect diffuse lighting, then adding indirect specular lighting from a cubemap is totally fine. If you need to, try writing out all of your sources onto a piece of paper and figure out which parts correspond to the rendering equation and your BRDF('s). This can help for making sure that you have the proper scaling terms (like 1/Pi for a Lambertian BRDF) and also for keeping track of which radiometric quantity is stored in your lightmap.
