Hey John- I know, I know, long time no post...
LifeWay is actually what was once know as the Suday School Board. It is absolutely an entity of the SBC, however it receives no direct funding from the Cooperative Fund. It encompasses a wide array beyond just the stores, as it has it's own in-house publishing house, various church consulting folks, etc.

As far as the stores, they are but a single area and don't necessarily exist to support the denomination. They have some autonomy to be entrepreneurial, but in my mind no way excuses the material they push. The state of the material in stores provides another commentary on the state of the denomination- giving no mind to the great heritage of Biblical reliance and the true Gospel; rather compromise the essentials and proper theology to make for a safe environment where the seats are full.