This subject is complicated and confusing. This is a simplified explanation. A lux measures light intensity. A lux is defined as a lumen per square meter. Imagine a lamp with adjustable focus. When the lamp is adjusted in width to a more concentrated ray of light, the total light flux (lumens) remains the same, but the surface illumination intensifies by one point (lux or candelas). The illumination can be measured with relatively simple tools. On the other hand, measuring lumens is much more complicated. The most common way is using a sphere that captures all the light emitted by a light source which is then measured at a fixed spot on the sphere, then via some complicated calibrations this lighting measurement can be correlated to light flux or lumens.