Lux is the globally standardised SI unit of illumination. It provides a uniform standard by which the amount of visible light present in a given space can be described. A lux rating is used to describe the perceived illumination of a known space, such as a room or a stage.
The lumen is the globally standardised SI unit of "luminous flux"--meaning that it measures just how much visible light is produced by an object such as, for example, a light bulb.
With clarity on the difference lumens and lux, conversion between the two is simple.
Lux is a measure of how many lumens are present in a given area. It's essentially a measure of "photon density" or "light concentration." A "denser" cloud of photons means there are more lumens present in a space--producing more brightness and higher lux. A "lighter" cloud of photons means fewer lumens--leading to dimmer conditions and lower lux.
To illustrate the difference between lumens and lux: While the sun always produces the same number of lumens, on cloudy days there are fewer lux outdoors. At night, only the lumens provided by the moon and stars reach the ground, leading to extremely low lux under a night sky.
To achieve a desired lux level in a given space it may be necessary to use many light bulbs, each producing a given number of lumens.
Measure the dimensions of the space that you wish to illuminate, and write down how many square meters of surface area it has.
Know what lux level you wish to achieve in that space. Consult lighting manuals or subject specialists to narrow down a good lux level for your application. For example, 500 lux is a standard moderate illumination level for an indoor room.
The fundamental ratio of conversion from desired lux level to required lumens is:
1 lux = 1 lumen per square meter. This is equivalent to: 1 lux = 0.0929 lumens per square foot.
To usefully convert from desired lux to required lumens, you'll need to know the radiance properties of your light (i.e., lumen) sources, their orientation in the room and other factors such as whether they radiate omnidirectionally (such as an open candle flame or unshielded light bulb) or have a narrower, directed beam (such as a flashlight or spotlight).