In "The Lagoon," how is it that Arsat and the White Man are friends?
In the story, Arsat is a young Malaysian man who previously fought alongside the English man (Tuan). According to historical sources, the British forces in Malaya traditionally sided with the indigenous Malay population against the Chinese and Indian populations. To cement its hold on power in the Southeast Asian region in the 20th century, the British capitalized on racial divisions between Malays, Indians, and Chinese.
Chinese rebellion against the British came in the form of communist insurgencies led by Chin Peng. Despite attracting a number of Malays into the communist fold, the Chinese often lost traction to the English. This is because the Malays largely saw the Chinese as a threat to their political and economic ambitions. Therefore, it was not unheard of for Malays to form alliances (albeit uneasy ones) with the British.
It is quite possible this is how Arsat came to fight alongside his white (English) friend.
He had known Arsat years ago, in a far country in times of trouble and danger, when no friendship is to be despised.
He liked the man who knew how to keep faith in council and how to fight without fear by the side of his white friend.
From the text above, we can see the friendship isn't a deep one; to the English Tuan, Arsat is a valued resource, nothing more. He listens to Arsat out of a sense of duty, and his nonchalance at Arsat's suffering betrays his true emotions regarding his Malay acquaintance.
He liked him—not so much perhaps as a man likes his favorite dog—but still he liked him well enough to help and ask no questions, to think sometimes vaguely and hazily in the midst of his own pursuits, about the lonely man and the long-haired woman with audacious face and triumphant eyes, who lived together hidden by the forests—alone and feared.
In Joseph Conrad's short story "The Lagoon," there is a cross-racial friendship at the heart of the story. Throughout the story, though, there is very little background information given about the characters in the story. Even the back-story of Arsat's love and escape is very sketchily told. As far as the relation between Arsat and the White Man is concerned, we are only made to know that the two of them came to know each other through some war and Arsat saved the life of the White Man when he was endangered in course of the war. In that respect, then, one can see the White Man's journey into the lagoon as a return-trip, driven by his sense of gratitude.