Blocking of the light could be a major problem. The article says its advantageous in that its an end to drive bys, but what if you wanted broadband in another room or even use your laptop in the garden, then you'd have to resort to a wifi unit surely.
Some aspects of this vaguely remind me of BPL broadband over power lines. That did seem good in theory, but it never took off. BPL could perhaps be a more realistic and at least current technology for remote locations.
The technical aspects of lifi are sparse.. Is li-fi basically BPL with the LEDs providing the method of communication between the nte and the consumer device. If so then I would imagine most home environments would not be suited to lifi.