It's a weird topic to try and discuss as it doesn't conventionally make sence... I say "lumens don't add".. and you say "so you're saying that if I put 4 lights in a room it's not any brighter?".. no, I am saying it would be brighter.. I'll use a really easy to understand example.
On my stove, I have 3 pots of water (all 1 liter), all at 100 degrees, and a sink. Now, for the sake of arguement, let's say they will remain at that temperature and not vary.
If I take one pot and pour it in a plugged sink the water temperature is 100 degrees and I will have 1 liter of water.
If I pour in the second pot (read second light).. I will have 2 times as much water but the temperature will remain the same.
To add the 3rd, of course.. 3 liters of water now, but the temperature will not be 300 degrees.
now instead of pot of water think 1000 Watt HPS.. and lumens are a temperature reading of the light.
The debate is mute anyway.. you need to consider wattage of light. Lumens are a reading of how humans see light in the spectrum. The different lumen ratings on bulbs reflect not the amount of light they put out.. it's the intensity of the spectrum at the given wattage. Humans typically see green spectrum light the brightest, so most flourescents are set for a lumen rating in the "green spectrum" so they APPEAR BRIGHTER TO HUMANS. A plant doesn't care about green.. it wants red and blue.. different lumens are rated on the bulb and now they call them cool white and warm white.. as the APPEAR TO HUMANS....
Now when lighting is discussed in terms of grow set ups.. typically you discuss it in wattage per foot of floor.. not how many lumens or candles per meter...
No they don't add, and it really don't matter, it's a stupid physics thing, and I'm getting tired of thinking about it.. I gotta go smoke a bowl before my head implodes.
Not to sound rude.. I just haven't had to use the noodle like this for a while and I'm starting to think a little more clearly.. I'll have none of that.