I don't believe that strict LOS is a requirement. If the room is getting ever so slightly brighter and dimmer, that's enough of a signal. Current wifi works down to -80dBm (or lower) which is a crazy small signal. -100dBm is a tenth of a picowatt of received signal strength.

I'm not saying that non-LOS is guaranteed by any means. But LOS isn't strictly required for this scheme to work. If only one light bulb out of 100 in a room is Li-Fi enabled it's going to be tough. If all three light bulbs in a room are Li-Fi enabled there's definitely hope.

The proportion of non-Li-Fi lightings to Li-Fi lighting is probably going to determine your SNR and thus your feasibility. Trying to make Li-Fi work with a 100 lumen bulb in direct sunlight is going to be a bad time since the sensor only has so much dynamic range. But if you increase the power of your light to be within an order of magnitude or two of the sunlight, you've got a fighting chance.