How does John Rawls' theory of justice reconcile with the ideas of liberty and equality???
I would say that Rawls' theory of justice is really based on the idea of protecting equality and liberty.
If a society were truly to use Rawls' "veil of ignorance" when making laws and such, it would have to protect everyone's liberty and it would have to do so equally. Under the veil of ignorance, you would not know what sort of a person you are -- rich, poor, black white. You would have to make laws and decisions without knowing who to favor. If you did this, you would certainly have to treat everyone equally.
Rawls also says that justice is only possible if one person's liberty is only infringed on in order to prevent it from infringing on the liberty of someone else. This is clearly compatible with the idea of liberty.