You haven't included the sentence that this phrase appears in or the greater context. As you have stated it, I don't see any reason why "our last week's meeting" would be incorrect. However, I wonder if your sentence included something like this: "During our last week's meeting, we decided that . . .." In this case, "our" is not necessary because of "we." It might also be unnecessary if the context is such that it is understood who was at the meeting last week. "During last week's meeting, the student council decided . . .." Obviously, the student council was present so it is unnecessary to use "our."
