Why Conway has no choice but to reveal about what he has learned about Shangri-La to Mallinson? (chapter 11)

Conway revealed the story of Shangri-La to make Mallison understand that Lo-Taen was lying to him.

It was the last thing he had ever intended to do, but he felt that in the circumstances it was justified and even necessary; it was true enough that Mallinson WAS his problem, to solve as he thought fit. He narrated rapidly and easily, and in doing so came again under the spell of that strange, timeless world; its beauty overwhelmed him as he spoke of it, and more than once he felt himself reading from a page of memory, so clearly had ideas and phrases impressed themselves. Only one thing he withheld —and that to spare himself an emotion he could not yet grapple with —the fact of the High Lama's death that night and of his own succession.

When he approached the end he felt comforted; he was glad to have got it over, and it was the only solution, after all. He looked up calmly when he had finished, confident that he had done well.