Knowing the number of lumens won't tell you whether it'll illuminate a fox at 100 yards. Lumens is a measure of total light output. If that light is spread into a wide beam, you'll light up a big area, but it won't light things up which are far away. The same number of lumens can be focused into a tight beam which will illuminate things a long way off. Of course, if two lights have the same beam shape, the one producing more lumens will light things up more brightly at the same distance.
Another problem with asking for a particular light output is, as several other folks have mentioned, that manufacturers tend to dream up whatever number they feel would help them sell their lights. They get away with this because total lumen output is difficult to measure, so consumers can't check up on the claims.
What you should be looking for is a light with adequate "throw", which is an indication of how far away it will light up an object with a particular brightness. This turns out to be easy to measure with moderate accuracy, and you'll find many posted measurements here and on flashlight review sites. The brightness of the main beam predictably decreases as the square of the distance, so if you know how bright it is at one distance you'll know how bright it'll be at all others. One lux is a dim light level, but a fox illuminated with one lux will be visible. So to get one lux at 100 yards, you'll need a light which produces 100 * 100 = 10,000 lux at one yard, or about 10,000 lux at one meter, the standard distance used for specification. A light which produces one candle, candlepower, or candela (all the same thing) in some direction has an illuminance of one lux at one meter in that direction, so you need a light producing a beam of at least 10,000 candelas at its brightest point.
There are only a very few readily available LED lights having that bright a main beam -- the most efficient currently available LEDs, when driven at their maximum rated power, will produce that light intensity only when focused into a pretty tight beam. One of those which does is the humble 2 or more C or D cell Mag light with a Mag drop-in LED bulb replacement. (Its main secret is its large reflector for tight focus.) Its light level drops by a factor of about 2 in the first few minutes after turn-on due to heat buildup, but it doesn't drop too much below 10,000. I'm not as familiar with incandescent lights, but I think that quite a few of the lights being recommended don't have that bright a spot. Now that you have a number to work with, you can do a bit of searching to find a suitable light.
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