In general, the answer is no, you don't multiply demand factors against each other.
Think of it this way: calculate connected load. They all add directly such that your service entrance has a connected load equal to the total of the connected loads on all the branch circuits it eventually feeds.
Then, there will be a demand factor that applies to each level of the distribution system. Usually, that demand factor would tend to get smaller as you go on up the chain towards the service entrance. That's because the service entrance will see the average power to the whole facility, and generally will not be so affected by localized peaks in demand here or there -- in other words, when power is peaking way over on the west side, it's most likely NOT peaking way over on the east side.
Your post leaves me with a couple questions, though:
1. NEC, in Table 220.11, in no case lists any lighting demand factor over 100%. Here in Chicago, the local code does require 125% demand factor for lighting, but I think that has much more to do with unions than science -- I can't think of any rational explanation for how the measured demand would exceed the connected load, and I'd never heard of a demand factor over 100% before I moved here. Why are you using 125% -- local codes?
2. "If I have a demand load (lets say for lighting) of 125% I calculate my demand and then I go ahead and multiply that total by the demand of 125%." Have you multiplied by 125% once here, or twice? Sounds like twice already. Maybe you meant to say that you calculate your "connected" (rather than "demand") and multiply connected by 125% to calculate demand?