I'm 99.999% sure that if there was ever an over-voltage to the lamps, the tiny little LED or the circuitry for it would burn out before the wire would catch fire. At that point, the LED/circuitry is the fuse and you have to replace it.
Now, really the only other thing that can happen is that the plastic separator between the lamp connectors could fail. This would result in a dead short, so it would trip the breaker in milliseconds. If you want to be 100% safe, then by all means fuse the lamps. All you really will be accomplishing is protecting the lamps. Everything else inside the box is just as susceptible to the same scenario of catching fire, even the connections to the fuse holder.
Think of it this way. Are there fuses on all of the light bulbs in your house? It's a matter of what you are wanting to protect really. If you want to protect every single item in your control panel against over-load/over-volt, then yes, you'll need to fuse every item individually.