What happened to the Buddha's speeches during his lifetime?

They were transmitted orally.

During the Buddha's time and that of other teachers, the dissemination of their teachings primarily occurred through oral means, involving discussions and debates. People of various backgrounds, including men, women, and possibly children, attended these discourses and engaged in discussions based on what they heard. Remarkably, none of the Buddha's speeches were written down during his lifetime. After the Buddha's passing (around the fifth to fourth century BCE), his disciples compiled his teachings during a council of "elders" or senior monks in Vesali, known as Vaishali in present-day Bihar. These compilations were collectively called the Tipitaka, or the "three baskets," as they held different types of texts.