What is the narrator's relationship to Lionel Wallace?

The narrator, Redmond, was in school with Lionel Wallace at Saint Athelstan’s. It seems apparent that the two had since become friends. However, throughout the course of the story it is difficult to tell how close these "friends" truly are. In their time together at Saint Athelstan’s, they were more like rivals than friends, and it appears they moved in different circles; Lionel remarks several times about how Redmond "didn’t come [his] way" and would not have been in the group that taunted him about the door. Despite this, it seems that Lionel views Redmond as his saving grace in a way, noting that "It was you—your beating me in mathematics that brought me back to the grind again” after a depressive episode resulting from his inability to locate the door.
In the present day, Redmond repeatedly expresses difficulty in ascertaining the truth of Lionel's story of the door in the wall. He is initially inclined to believe his friend, demonstrating a degree of closeness. However, he then begins to doubt the story, no doubt due to its fantastical nature. As the story closes with news of Lionel's death, Redmond is certainly affected. He states his mind "is darkened with questions and riddles." It is worth noting that although Lionel's death troubles him, he does not appear to be wracked with grief, as might be expected of a close friend. Instead, his reaction seems more akin to their initial relationship: boys attending school together, mostly moving in different circles. As a closing thought, Redmond ponders on Lionel's perception of the world, which may have affected his perception of their relationship: "By our daylight standard he walked out of security into darkness, danger and death. But did he see like that?"
https://www.shortstoryproject.com/story/the-door-in-the-wall/

The narrator's an old school friend of Lionel Wallace. They attended St. Athelstan's College in West Kensington, London. When the narrator, Redmond, started school, he was very much Wallace's co-equal. But Wallace soon blazed ahead of him, racking up an impressive collection of prizes and scholarships. He's just one of those pupils who seem to be good at everything, whether it's sports or academics. This makes it all the more astonishing that someone like that would retreat into a world of fantasy and delusion. Wallace seems to have everything he could possibly want in this world, the world of the ordinary and the everyday. There seems no need for him to construct his own little fantasy world, from which to escape the real one.