Neon has been around for a very long time in cyberpunk narratives. LED seems like the way to go according to some of the responses - any other viable candidates?
If you take a look at the original Blade Runner movie, you'll see a lot of the older buildings with pipes and equipment all running around the outside of the building. This was done by design; the implication of this was that the society was decaying and as humans left for space what was left of the inhabitants needed a utilitarian approach to their environment. That is to say, that it was far more efficient to retrofit modern equipment onto old buildings than knock it down and build something new where the modern equipment was integrated by default.
If we take that model and apply it to lighting, then neon (in the form of fluorescent tubes and the like) work as a retro style, but in reality LED bulbs are the ultimate form of retrofitting in that they take a super efficient lighting system and build it in such a way as the installation of it is as simple as changing a bulb.
The problem with neon in a cyberpunk society is the efficiency of use; it'll be the efficiency of production. Most cyberpunk environments are crowded, consume massive amounts of energy and other resources, and are designed to reflect a need to reduce consumption in some way while also giving off that 'tech' feel. In the 80s, fluorescent tubes and bright neon colours represented that very well and stylistically still works to the point where we tend to equate bright backlit colours with the future somehow. But in reality, LEDs are going to be easier to make, and better in terms of energy consumption.
If you want proof of that, before LED bulbs fluorescent tubes were also retrofitted into conventional bulbs, and are now being replaced by LED bulbs. in most homes. The reason is cheaper production and less energy use. They are also more versatile and mobile which is why most torches now use them instead of small incandescent bulbs.
As an aside, the reason why LEDs have risen so dramatically as a lighting option is the invention of the blue LED. Red and Green LEDs had been around for some time, but it was the blue, high energy LED that could be mixed with red and green to generate enough luminous energy to actually see by (instead of being an indicator on a computer) that allowed their uptake in this regard.
In any event, LED lighting is what I would expect any cyberpunk dystopic future to use, even if it doesn't suit the style that world is actually going for.