We need to answer the questions given ---- the end of the lesson.

The correct preposition is: at

Here's why:

• At indicates a specific point in time. In this context, it refers to the conclusion of the lesson, which is a fixed point.
• About is used for a general period or topic. It wouldn't be specific enough to answer questions.
• By suggesting a deadline or limitation. While there might be a deadline for answering questions, "at" is more natural for the specific time of the lesson's end.
• On can refer to a date or a specific day. It wouldn't be appropriate for the timeframe of answering questions within a lesson.

Therefore, "at" best indicates the specific moment when the lesson ends and question-answering is expected.