Lumen is the unit for the luminous flux, or light output, of a lamp. This provides information about the brightness of the lamp by measuring how much light the light source actually emits. The higher the ceiling, the more lumens are required.
Lux is a unit of illuminance. It measures the amount of light reaching a surface (for example, the floor or your desk). Lux can therefore be expressed as a certain amount of lumens per m2.
An example:
A 500 lumen light source illuminates 1 m2 with 500 lux.
Should this light source illuminate not 1, but 10 m2? Then the light source illuminates 1 m2 with (500:10=) 50 lux.