I turn on a single 90watt light bulb, and measure the lumens at a set distance.
Then I replace the 90watt with 2 45watt light bulbs, and measure
Finally, I replace it with 6 15watt light bulbs and measure.
Assuming constance distance, and lets say incandescent bulbs for all of them.
Will I get a reading of the same lumens?
If light bulbs of different wattages all had the same efficiency for turning electricity into visible light, then the answer would be yes, you’d get the same illumination at any given distance from those situations. In actual fact, higher-wattage bulbs tend to be a bit more efficient, so you’ll probably get more illumination from the single 90 watt.
Probably not. Lumenous output will vary between incandescent bulbs of different wattages, even assuming that each bulb has the same type of coating (clear, frosted, soft light, et cetera). It’s probably relatively close–certainly within a close order of magnitude–but not an exact measure, with higher wattage bulbs being more efficient.
With fluorescents this goes completely out the window, because the spectrum of fluorescents is almost exclusively restricted to visible light, whereas incandescents waste much of their energy generating heat.
Or, upon preview, what Chronos said.
Stranger
If you started out by using the number of lumens produced by each, then things would work out as you describe. Even if the lumens were spread over somewhat different spectra, all these systems are linear so their sums would also be linear. Or if you posed the question you did but wanted to know how many watts of power were consumed, it would also work out.
You would, though, have to make sure that you had the same access to all the little bulbs - that is, they can’t be hiding each other.