Juvenile records are sealed and not generally available to the public. If in fact the murder was completely handled through juvenile court that alone cannot preclude the Illinois State Police from issuing the FOID. If the police are claiming he lied on the application I would be interested to see what proof they have. Since the record was sealed it will be impossible for them to attempt to use the previous juvenile prosecution as evidence for any new felony charge. The police can always arrest a person for anything - whether its right to wrong. When they do it wrongfully it may result in civil liability against them for deprivation of one's civil rights. Did he actually get charged wtih any new offense? www.papc.bizAsk a similar question
Sealed records are available to the State Police. Sealed means the records are not publicly available.
Lying on a FOID application is an offense that must be done "knowingly," which is a difficult standard for the State. If your relative believed his juvenile history didn't matter and they did not have it in the record there may be some wiggle room.
Additionally, there is a disconnect between Illinois law and that of other states. In Illinois very few murder charges are handled in juvenile court. It may not occur to an Illinois State's Attorney this is even possible.