Q: What is the severity of one showing their private parts to somebody in public?
Q: What if the person does not want to forgive that individual/s for that lewd act?
Q: Is it justifiable for a person not to forgive?

Answer:

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You are the best of the nations raised up for humanity; enjoining what is right and forbid the wrong and believe in Allah; and if the followers of the Book had believed it would have been better for them; of them (some) are believers and most of them are transgressors. 3:110

As Muslims, we called upon to be our very best in all do. To instigate wrong on any level would be wrong in itself. To sanction wrong is against our belief. We are called upon to prevent ourselves and others from forbidden actions. It is forbidden for a male to intentionally expose from the navel to the knee to a stranger, likewise, it is also forbidden for a female to expose from the neck to the ankles to a mere stranger. According to the Hadith, a simple way to stop people from continuing lewd actions is to talk to them in a gentle manner that inspires then towards positive change. We should use peaceful methods to bridge all moments of tension, so as to facilitate peace and reinforcment of good Islamic behavior. Should this fail, it would be best to pray for such individuals.

Rasulullah (sallallaahu alayhi wa sallam) has stated that Haya is part of imaam. Also Rasulullah (sallallaahu alayhi wa sallam) has stated: When modesty is lost, then do as you please. People that lack modesty lose direction of distinguishing between the good and degrading. In the process, they relinquish an important part of Islamic life, in the process they also give up a significant portion of faith.

If a minor exposed their private part, then the minor must be sat down and spoken to as to their distasteful deed. If a sane adult had exposed himself to another person, then not only would it be a sin, but it would be necessary for the person to seek forgiveness towards the victim.

As for forgiveness, Rasulullah (sallallaahu alayhi wa sallam) stressed its importance. Although one has a right not to forgive, forgiveness would create less pain for the wronged (victim). To hold a grievance only limits oneself to attaining maximum spiritual strength. Each person at some point has possibly wronged another. Should each restrict their forgiveness to situations that they deem fit, greater hostility would continue to exist within members of society. Thus the quran and hadtih stress the significance of forgiveness. To forgive is to liberate oneself.

Should one insist on not forgiving, then on the Day of Judgment, the perpetrator of wrong would be called upon to relinquish a portion of their deeds towards the victim.

Allah Certainly Knows Best.