When speaking of justice wrt 2 or more people, it will always be imperfect since there can never be 100% agreement. Justice is really a personal thing when it comes down to it.
Is it 'just' that we should all be born sinners and spend eternity worshipping and serving a being who isn't our equal? If an un-just God is our example, there's no hope in hell of us acheiving true justice as we define it.
Now this would depend entirely on what you mean by "justice". Do you define it in accordance with the aforementioned dictionary definition? Or do you mean a higher form of Absolute Justice? I personally think that only an all-knowing creator can give us "Absolute Justice". (And note that well - all-knowing and one who created us.) We, as people, all suffer from flawed thinking, lack of omnipotence, omniscience, etc. So we can only deal out justice according to our "lowly" human standards. And as times change, so does our perception of "justice".
According to the Old Testament, "justice" in human law (for crimes) followed the old "eye for an eye" principle. That has now changed to something less brutal, which people might term "humane". Previously we may have considered it justice murdering a homosexual for having sex with a man. Or burning a woman for having three nipples. Now we don't - we try to give these people equal rights.
So yes I believe justice exists without God: but like humans it remains flawed, temporary and ever-changing.
Of course, rereading this in " mode " fills me with questions about God creating us. Why, simply because He created us, does God have any right to judge us? Does this not strike people as somewhat of a dictatorship? Does a God-led democracy even seem feasible?
We may have children, but surely this doesn't automatically give us a right to judge our children and mete out "justice" for what they did with their lives? So why can God do so? Or have I started to question Him from a mortal viewpoint again?