An apartment complex says that they can put a lock on the washer and dryer to prevent usage, is there a way to unlock it?

Yes it is called criminal damage to property or criminal trespass, since if the usage is not included or for some reason they are not allowing you to use it without doing certain things, If you go past the security on a item you are not suppose to be using, then you start a criminal act.

You did not give any info as to if they can lock it legally from you, but even if they lock it illegally, that does not give you any right to do anything but sue them in court for the use. The difference between wearing or not wearing those matching police braclets is doing things the legal way or the way people want to do it