There is no way to directly measure lumens.
Lumens are CALCULATED from the lux, and, that lux has to be measured in a device that spreads the lumens out evenly, so that no one spot is brighter than another. (The device is called an Integrating Sphere (IS), and, amateurs attempt to approximate this with various homemade versions. )
A LUX measurement is then made of that homogeneous light, based upon the assumption that all areas measured yield the same lux reading as the light is homogeneous.
Lumens = Lux per square meter, so, knowing the surface area if the IS (the square meters), and the lux, you can CALCULATE the lumens from that lux reading.
In real life, without a real IS, its actually almost impossible to get a truly homogeneous distribution of light, and, therefore, depending upon the exact spot chosen to measure, the lux levels tend to differ, which changes the calculated lumen estimates.
So, other than using an IS, there is no DIRECT way to convert lux or cd to lumens, any more than you could DIRECTLY convert speed to horsepower. (You'd need more information, and then be able to calculate it, etc...)