There is a difference between a fan and a compressor: the one provides thrust, the other compression. In a turbofan engine, there are separate sets of blades to do each job.
The Lilium's ducted fan is an example of a wider class of ducted propulsor. They all work the same way, to accelerate air in one direction so that the reaction force pushes the fan or propeller in the other.
If the blade disc were used to provide compression, the device would not be a propulsor but a compressor and would not exit to the free air stream.
Blade aerodynamics being equal, the maximum potential thrust is determined by intake diameter, which is obviously rather small: a single device would power a 3 m (10 ft) span model plane quite nicely.
Stacking up crazy numbers of small fans obviously increases total thrust in proportion, but it is less efficient than a couple of big ones. Integration with the airframe aerodynamics, especially the wing, is critical. It was studied intensively about half a century ago, such as for the Vought ADAM V/STOL jetliner project (illustrated article here). One can at least say that the Lilium configuration is not optimal (there was a question about exactly that a couple of months ago, if anybody can find it).