What does "God is just" mean according to Calvinists? In our world, what we understand about "justice" is not just a verdict between guilty or not guilty, because it also balances the punishment on the severity of the crime.

Here is an illustration: 
There are two people who are not elected before the foundation of the world. 
The first is a 16 years old kid who was naughty and sometimes disobedient to his parents who then died. 
The other one is a 30-year-old man who raped many women and then died.

The question is, does the Bible say that, because God is just, both of them will have the same punishment tormented in the lake of fire eternally? What is the Calvinist position?
You are correct in noting that in Calvinism one's ultimate eschatological end is the result of either God electing one to glory or one to destruction.
However, because Calvinist care about what Scripture teaches, they also hold to the belief that their are varying degrees of punishment (and supposedly varying degrees of glory) rendered individually to each man.
Here are a few obvious passages which strongly suggest gradations of punishment in hell.

[God] will render to every man according to his works. (Romans 2:6)
[This is the conclusion of one of Jesus' parables.] The servant who knows the master's will and does not get ready or does not do what the master wants will be beaten with many blows. But the one who does not know and does things deserving punishment will be beaten with few blows. From everyone who has been given much, much will be demanded; and from the one who has been entrusted with much, much more will be asked. (Luke 12:47-48)

One popular Calvinist outlet, Ligonier Ministries, defends this belief with no qualms.

There will be degrees of punishment during the day of wrath. One “trivial” sin makes us guilty of the whole law and liable to eternal torment (James 2:10). Yet some acts are worse than others and deserve harsher punishment (Num. 35:9–29). As bad as Sodom was, her sentence will be lighter on Judgment Day than Bethsaida’s because Sodom never saw Jesus (Matt. 11:20–24). The sinner who never hears of Christ will go to hell, yet his pain will be less intense than those who hear the Gospel each Sunday and refuse to repent.

So then, does the Bible say that, because God is just, both of them will have the same punishment tormented in the lake of fire eternally? The answer is no from a cursory reading of the Bible, and the answer is also no from a normal Calvinistic reading of the Bible.
Though your question seemed to imply that you're wondering what justice means to a Calvinist. I would suggest clarifying exactly what it is that you are asking. For self study on this subject, look into forensic justification and double imputation. Those who fail to have Christ' righteousness imputed to them are left with Adam's sin and their own personal sins left imputed to their own accounts. You ultimately get what's imputed to you, and the more grievous the sin that's imputed to you, the more judgement you receive.
Source: https://www.ligonier.org/learn/devotionals/degrees-punishment/