This is some very interesting reading that has so many ways out of it, if you are creative enough to think of them.
The mayor has outlawed Lightbringers "costume-brand vigilantism", making it illegal for him to go around in a costume and enforce the law within the sight of police officers or risk being arrested, and has been ordered to turn himself in. If you look at things Lightbringer is enacting citizen's arrest on criminals, but wants to remain anonymous so hides his identity with a mask. Both of which are in his right to do, depending on the laws of the land since every place on this Earth has its own set of laws. ( Such as one of my favourite laws to point out as unreasonable as the law that makes it illegal in some parts of Texas to engage in sexual acts that do not result in a child or children, which was used against a gay couple to make the police breaking into their home legal and charge them with wrong doing. Police got a complaint of loud noises coming from the house by a neighbor, so they broke in thinking that someone was in trouble only to find a gay couple engaged in a sexual act. So they arrested the couple on the original charge of disturbing the peace, and then after some research the state brought up that old law; which was originally written to prevent acts of bestiality and used it in the context of consensual homosexual sex. )
Going back to the citizen's arrest subject, which many people may be aware of and states that a citizen of a jurisdiction that is not a member of law enforcement is allowed to arrest a criminal in the jurisdiction that they reside. It is an old law that has been around for generations and has been invoked many times, but it does open up a whole other can of worms when used. This is because it opens the person up to being sued for false arrest, kidnapping, assault, and a whole host of other charges that could be brought against them if it is found the civil rights of the accused were violated. But we don't know if this law even applies in Pharos City since laws are different from city to city and country to country, and we don't have access to all the laws that they have. It's not like it is written somewhere... Unless the wonderful creator actually has a book somewhere where he's written down every single law of the city, and has it tucked away under a green cushion next to morpher. ;P
Now, if it is legal for someone to invoke citizen's arrest in Pharos City, then that could be one way out for Lightbringer, but that also leaves him open to legal retribution since a criminal can charge him with wrong doing or violating their civil rights. This has been addressed before when Lightbringer was brought to the stand as a witness for his part in the FBI's operation against the Slavers. Thanks to the legal foot working by his lawyer he was able to get around letting everyone know his identity and assert his legal rights to use a mask to protect himself and those he knows from retribution by other criminal elements. Maybe she can do some more and get him out of this hornet's nest that the Mayor has stirred up, but then there are the others to consider and the other ramifications of such a broad law that the Mayor seems to want to put into effect. Sure she is targeting Lightbringer and his associates, but what is to stop others from being associated with them just for doing the same things or just from being inspired by them? We've already seen in past issues that others around the world have been inspired by Lightbringer to use their abilities for good, so who is to say that next it won't be one of them that the law goes after.
Lightbringer might have started out with just wanting to protect and work on one city, not trying to change the world. But like many other things, what happens in one city can spark a global change. I'm sure that Archduke Franz Ferdinand of Austria would agree with that.