Lux indicates the intensity at a given point, while lumens indicates the total "amount" of light.
Measuring in lumens would be a good choice for say fixed lighting fixtures in rooms and other similar indoor or outdoor locations where the light is meant to evenly illuminate an area. For flashlights, lumens would also be good if the beam profile is 100% spot or 100% spill, then we can have a good idea of the intensity because there is no variation in intensity throughout the beam profile.
The majority of flashlights have beam profiles which are made up of a hot spot and spill. If measurements are given in lumens, we do not get an accurate idea of the intensity of either the hot spot or the spill beam. Instead we will need to estimate and roughly divide the hot spot and spill values base of the total "amount" of light given out which was measured in lumens.
So by having the output values in lux, you can get direct intensity info of the hot spot and flood without the need to estimate or guess. All lux measurements are taken at 1 meter.
Spot lux measurements are taken at the absolute center as illustrated where the red lines cross in the image below:

Spill lux measurements are taken between the absolute center and outer edge as illustrated where the red lines cross in the image below:
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