Lumens, as mentioned, are part of the specs to consider for out put. Cd is the other light related spec.
Essentially, the overall goal of a weapon light is to do some combination of allowing you enough light to aim the weapon, enough light to identify the target, and enough light to identify the target context.
So, you start typically with a consideration of what the maximum range of the target scenario would be...as you want your light to be able to illuminate it at least at that range.
So, if you want the scene illuminated at 50 meters, or 150 meters, or 500 meters, etc, that is the starting point, as that starts the first step in knowing what cd you want.
The second step to know what cd you want is the use of that illumination. Is it just to aim with, or, will it be held on the scene to allow either aiming, and/or watching the subjects/targets in case one wants to make a break for it/go for a weapon, throw evidence into the bushes, etc.
The further away the subject, the more light, proportionally, is needed to resolve details. the reason has mostly to do with the part of your eye NEEDED to resolve details having the WORST night vision/low light capability. This is also the part of your vision you aim with, the fovea.
MOST people need ~ 1- 5 lux on a target to aim at it at long ranges...depending on the scope, their night vision/adaptation, the target's contrast, etc.
To get 1 lux on target, you need a light with a cd that is the square root of the needed distance, in meters.
So if you need to get one lux on a target 200 meters away, you need a light with a cd of 200 x 200 = 40,000 cd.
To get 5 lux on the same target, you'd need 5X more cd...or 200,000 cd, and so forth.
OK, so lets say you have now decided on the range, and the lux on target AT that range that would make sense...
...You now look at the use in terms of the size of the beam/width on the target at that range.
If you want to only aim, you can have a very tight beam that just puts light at the cross hairs. If you want to be able to see if someone might be moving across the line of fire before they are in the way, etc, and/or want to have a small gang of perps lit up to make sure they are behaving, or not, you might want a beam width that is a lot wider.
This is where the beam ANGLE comes into play...as that dictates the width of the beam at any given distance.
A quick way to estimate the beam width you want is to pick a width at a given range, and then divide it by 0.018 x that range....
IE: You decide you want an at LEAST 10 meter wide beam at a 100 meter range....
..so you take 10 m/(0.018)(100 m) = 5.5º beam angle (Minimum beam angle to GET a 10 m wide beam at 100 m range).
You THEN look at if a WIDER beam would hurt anything...and pick an upper beam angle range if appropriate, and otherwise just be sure the light has at LEAST the minimum beam angle.
OK, NOW you know the beam angle, and the cd needed.
If you want to ALSO specify the LUMENS, think about WHAT you will then use the lumen spec FOR?
Remember that it takes a LOT more lumens to paint a larger surface area (Like a flood light)...and a teeny number of lumens can make a small bright dot of light (Like a laser pointer).
If you think of the lumens as what your light sends OUT, and lux as what bounces back to your eyes...you will get the important part of the relationship. Essentially, you can't SEE lumens, only Lux.
If you imagine that lux is like the DEPTH of water, and the deeper the water, the brighter the target will look to you...and the lumens are the TOTAL water the light can send out...
Imagine that you have a shot glass of water...and its bout an inch deep or so...and you look down into that shot glass, and see that inch of depth as a certain brightness.
Now, pour that shot glass into an empty wading pool, say about 3' wide. How DEEP is that same water, and how bright will that SAME number of lumens look to you?
Its no where near an inch deep anymore, its barely a thin film of a puddle in the pool. The same lumens would essentially go from bright to dim.
So how MANY lumens is "ENOUGH"?
Why even ask?
You only need to use the cd/lux for a weapon light output...as that tells you what you are actually trying to evaluate as far as output, and the beam angle to narrow the selection down to the intended task.
The 500 L Fury for example, as mentioned aways above, is a popular indoor/short range weapon light. It can light up a wide area at once, for situational awareness, yet have enough lux on target to aim with. If it was 1,000 L, it would work even better of course....as we already know the beam angle has proven useful.
When the Fury would be less useful is where you and your compadres might be in a proximal firing position, and the spill from your light might illuminate THEIR positions. Then, you might want a light with little to no spill, to make YOUR position a simple point of light, but w/o context to those your light is shining AT. That way, if you pop and move, they don't have a picture of to where that might be to, etc.
And so forth.
So there is no lumen number, in of itself, that's "Enough" or not enough, etc.
You really need to think about the ranges and uses of the light at those ranges, to start the process....and go from there.