You have to take control of exposure away from the camera and give it to yourself. Cameras will look at the total scene and try to make it appear a medium exposure value. Most cameras can't tell the difference between a black cat in a coal mine and a white cat in a snowstorm. They will try to make both of them medium gray.
The reason the lights are all appearing the same color is because they are all being overexposed. The way digital cameras work, there is only a maximum brightness the red, green, and blue channels can each measure. If all three channels are at full brightness as measured by the camera's sensor, you'll see the same color: white. It matters not if there's three or four times as much green as there is red and blue in one of the lanterns, if all three channels reach full saturation as measured by the camera that lantern will look white.
To see the colors of direct light sources in most scenes you must reduce exposure significantly. When left to determine exposure automatically, most cameras will assume it is perfectly acceptable to blow out the direct light sources in the scene in order to show detail in the surrounding areas that are much darker.