We are using LED rings from superbrightled and Neo_pixels, for decoration on our robot. Are we allowed to control the lights with an arduino (not connected to the roboRiO)?
Yes, non-functional decorations are allowed to be controlled by third party devices. R68 only applies to motors/actuators.
You probably already realize this, but most of the bright LEDs require 12V, which you can’t get from an Arduino, and even if they’re 5V, you can’t light very many due to current limits. 12V relay modules are available starting under $5 from many electronics/robot vendors and even Amazon which can be easily controlled from an Arduino.
Depending on how bright your LED’s are, the “Limelight ruled illegal” thread may be relevant to you. It would also be a good idea to study the Game Manual to see what it has to say about bright LED’s.