By the time the lecture ended, most students (had left/ left) the auditorium.

In this sentence, two actions occurred in the past: the lecture ending and the students leaving. The phrase "By the time the lecture ended" indicates that the action of students leaving was completed before or at the moment the lecture concluded.

When describing two past actions, and one action was completed before the other, we use the Past Perfect tense (had + past participle) for the earlier action and the Simple Past tense for the later action.

Here, the students leaving the auditorium happened before the lecture officially ended. Therefore, "had left" (Past Perfect) correctly conveys the action that was completed first, while "the lecture ended" (Simple Past) describes the subsequent or concurrent past event.