Will a 15 amp circuit support the lighting I plan to install?
It looks like you have spent some time and research working on this, well done. We calculate general purpose outlet for dwelling units at 180 W/VA or 1.5A per duplex receptacle. If you have an NEC handbook illustration 220.4 is a great example. 

The lighting is a bit of guess work and since we already know the outlets it would be safe to use 1.5 W/VA per square foot of living area to determine the load. Understand that the NEC isn't interested in what you are installing, it's interested in what may be installed by whomever at a later date. 

That being said. I don't really see a problem with your thinking, but I do have one question. Are any of these receptacles being used for a specific duty such as a refrigerator or microwave or such. If so they must be calculated at the nameplate rating rather than the general purpose 180W.

My final thought is why not just run all 20 amp circuits and that would insure you for expansion or if you missed something. We call it Value Added Resource. For minimal cost it may pay off in the end.