Draw a small amount (30mA, burst to 300mA) of DC (~5v) power from 2-wire wall switch?
Why not consider placing your small Arduino board and its power source in the electrical box where the light bulb is located? 

From your diagram it appears that the powered 220VAC feed and return line are both in the electrical box at the light fixture. 

Edit to Add an Alternate Idea to try out. There is too little data regarding the Lifx bulb to know if this is even feasible at all. So you would have to simply try it.

The idea is to remove the wall switch from the AC circuit and instead wire it into the MCU board. Then wire a small transformer across the AC lines that come to the switch box. This would likely have a low turns ratio and would operate off the current that passes through the special LED bulb unit. An AC power converter on the other side of the transformer would convert AC to DC power.