It depends on what information you are trying to emphasize. If you are trying to identify a specific speaker — for example, there was one American speaker and one Russian speaker — you would use the specific article “the” to make clear that you are talking about the American’s speech: “The American teacher’s lecture emphasized the importance of collaboration in the classroom.” On the other hand, if you are not trying to identify a specific speaker, but you want the reader to know that the speaker was American, you can use the indefinite article: “An American teacher’s lecture emphasized the importance of collaboration in the classroom.”

A lecture by an American teacher.