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. This measures the amount of light that reaches a surface (for example the floor or your desk). Lux can therefore be expressed in a certain amount of lumen per m2.
Just an example:
A light source of 500 lumens illuminates 1 m2 with 500 lux.
Does this light source need to illuminate not 1, but 10 m2? Then the light source illuminates 1 m2 with (500: 10 =) 50 lux.