Lord of the Flies is a novel about a bunch of children (boys) left to fend for themselves. This story began with fear. They crashed into an isolated island with no adult supervision or help. Fear is everywhere. The forest is dark and noisy at night. They're all young enough that the dark alone is scary to them. Many have nightmares--the crash alone should be scary enough for their dreams at night, let alone the thought of never being found.
Fear is also in the way the boys slowly turn savage. Jack uses fear to guide the boys into his tribe. He will "protect" them. He will provide meat/food for them. These are adult promises, so the boys join to avoid their fear. When they stop fearing is when Ralph and Piggy are in real trouble. If they have no more fears (like they do in Jack's tribe) they are dangerous.
Fear is also within Jack's tribe once he has almost everyone in his tribe near the end of the novel. He punishes Willard in chapter 10 just because he can. So there is again fear within his tribe.
The most obvious fear is with the dead man on the mountain. The boys think there is really a physical beast there with them. It's only them, which can be even scarier--especially for someone like Simon who knows that from the get go. By the end, even Ralph is without hope. They have smoked him out of the forest, and then all fear for him is gone when the officer rescues them.