Lumen is the measurement/output of light produced from a lamp.
Lux is the measurement of light at a specific point or position.
Lumens can be split into 2 groups: Raw Lumens & Effective Lumens
Raw Lumens is the light output quoted by the manufacturer of the LED.
Example: Cree XM-L2 10w LED has a Manufacturer Raw Lumen figure of 1050 Lumens. If you have 8 of these in 1 lamp the Raw Lumens for that lamp is 8 x 1050 = 8400 Lumens Raw.
Effective Lumens is the actual measured Lumen figure that takes into account real losses e.g. Thermal loss, Optical Loss & Assembly loss.
Example: Thermal loss, Optical Loss & Assembly/Circuitry/Electronic loss, can equate/effect up to 25% typical lumen loss eg: 8400 Raw Lumens = 6300 Effective Lumens. Other lighting companies have up to 35% Lumen loss due to bad thermal designs, bad housing designs and cheap optics.
Lux is a world-wide term for the measurement of light on a specific surface. It requires the use of a lux meter which measures the light output. 1 lux of light is equivalent to a full moon at night in good atmospheric conditions.