All the sentences are correct. I've never heard reference to a teacher's table, although the phrase makes perfect sense.
You can also refer to the lectern as a podium.
1. The professor stood at the lectern and gave his lecture.
2. The teacher stood at the teacher's table and began to teach.
3. The teacher stood at the lectern and began to teach.
4. The teacher stood at the lecture table and began to teach.
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Are they al correct? What other words can we use? Which ones are commonly used?
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