A warning regarding small continuous light (be it LED or halogen): they are not as powerfull as an external flash unit. That means that you will be forced to place the LED light quite close to the subject, otherwise you must increase aperture, raise ISO and/or decrease shutter speed.
If you decide to buy a flash unit, take into account that, using it in TTL mode, the Nikon system (i-TTL) is different from Panasonic/Olympus: there is no such flash unit that works in TTL for both systems.
But, if you plan to use de flash unit in Manual mode, any (low voltage) flash unit will work for any system (except -previous- Sony).
It looks like Olympus flash units -similar to Panasonic ones- are cheaper.
An aditional advantage of an external flash unit with a pivoting head is that you can bounce the light of walls or ceilings, producing a much softer and directional light (than the one produced by the pop-up camera flash).
A second advantage is that LX cameras series have the ability to synchronize flash at all shutter speeds. That means that being outside under bright sunlight, you can shoot at 1/2000 second with flash light filling nicely shadows (in this situation a led light is completly useless).
Hope I have shed a little light