Actually there are eventually going to be arcs where the League will be asked to help design and oversee the project. 

In my head the prison (which needs a good name) is going to be an Island Prison or Underground prison that has advanced technology and somewhat brutal guards that draws a lot of controversy due to being compared to Guantanamo Bay due to things like alleged civil rights violations, staff corruption, and illegal experiments. So basically Arkham yeah. 

Though in the comics they always freaking break out no matter what Batman does so who knows :P