If they are guilty of the crimes that carry that penalty, yes.
There are a few adolescents that have carried out horrific crimes, and they should never be allowed to interact with the public again. Most serial killers start showing signs of their behavior and mentality in adolescence.
Unfortunately many YES.
Even a child knows the difference between right and wrong in terms of serious crimes that would involve such a punishment .. And that committing a haneous crime has consequences. An adolescent knows and comprehends the severity of consequence in terms of something so sinister that it may involve their entire lifetime. So in answer to the question .. YES, the punishment should fit the crime.