The point of view from which "The Lagoon" is told is that of an omniscient third-person narrator. The characters, including the white man and Arsat, are referred to in the third person, so they are not narrating the tale. In addition, the narration is all-knowing. For example, at the beginning of the story, the narrative reads in the following way:
"For the last three miles of its course the wandering, hesitating river, as if enticed irresistibly by the freedom of an open horizon, flows straight into the sea, flows straight to the east -- to the east that harbors both light and darkness."
This type of detail is supplied by a narrator who knows the shape of the land and the river, something that is likely beyond the characters who are poling down the river.
The narration also includes details about the natural world that only something or someone who is all-knowing could have access to. For example, as Arsat is telling his tale to Tuan, the narration reads as follows:
"A breath of warm air touched the two men's faces and passed on with a mournful sound -- a breath loud and short like an uneasy sigh of the dreaming earth."
The narration has access to the functioning of the natural world and almost seems to understand the natural world. For example, the narration includes the sound that the air makes as it moves beyond the men's faces. It is as if the story's narrator has access to the secrets of nature; therefore, the point of view is that of an omniscient and unnamed third-person narrator.