1) When an individual does not have to answer for or accept societal punishment or consequences, it becomes much easier to lose a sense of morality or responsibility.
2) A good society depends not only on a solid governing system but also on the moral shaping of each individual.
Which do you think would be easier to develop on or find direct quotations from the book showing it?
These are both very insightful statements regarding the text of Lord of the Flies. The first thesis is easily supported by evidence in the novel. The longer the boys go without an organized system of "moral order" the more chaotic and savage their behavior becomes. Proof is found in a comparison between the boys' behavior at the opening of the novel and at the end.
I would prefer the second question: it seems to me easier to structure an answer to. You would need a section on what is a "solid governing system" - this would be a great place to introduce what we know about the social and historical context - the discipline of the boys' school and teachers are referred to in the novel - the governing system installed by Ralph and the imagery of the conch which becomes increasingly fragile can then be set up as a comparison. The logic would guide you to show that the system set up on the island is not "solid" and therefore led to the violence. An interesting point may then be to bring the war into the essay - both the cold war and WW2 as conflicts caused by a "solid governing system"
Your second section would then require a series of character analyses to show the moral shaping of each individual and track the changes through the novel: Jack and Roger's increasing sadism; Ralph and Simon's increasing weakness and vulnerability. You would need to explore the fact that the society fails despite the apparent moral strength of some of the characters.
Clearly the essay is inviting you to discuss the image of the Beast and the Lord of the Flies - the inherent weakness and selfishness inherent in us all - and Simon is your best source of quotations on this. Again, the cultural echoes of the novel with Genesis and the Fall - the concept of original sin - could be introduced as part of such a wider discussion.