If "fast lanes" means "lanes for cars that are faster than most of the other traffic," then yes, fast lanes are legal.
But establishing them does not suggest you are permitted to speed; it merely acknowledges that some cars move faster than others and that slower cars impede the flow of faster-moving traffic. Preventing faster cars from passing slower cars creates traffic congestion, and traffic congestion increases the risk of injuries and property damage. The laws are meant to reduce the likelihood of those harms by managing the flow of traffic.
Of course, this doesn't necessarily have to involve speeding. If the speed limit is 70 MPH, a truck going 55 should move to the right if other cars are going 60.
But even if it is an acknowledgement of speeding, a law that acknowledges a crime by requiring others to help reduce the resulting harm isn't permission to commit the crime. A law requiring police to process rape kits isn't permission for you to rape anyone, a law requiring teachers to report child abuse isn't permission for you to beat your children, and a law requiring the government to prepare for a nuclear attack isn't permission to detonate a dirty bomb.
These are all just laws meant to help the government manage foreseeable problems.