My textbook translates it to that, why not use 講義 instead? Would it be wrong to use either, also what are the nuances?
漢字の講義 and 漢字の話 are both correct Japanese phrases. 漢字の講義 sounds like a serious and academic lecture (usually oral). 漢字の話 is vague, and it can possibly refer to a column, a trivia, a discussion, a long talk, a lecture, or an entire book. See broken laptop's link in the comment section. You can translate 講義 to 'lecture' without thinking much in most cases. However, when you translate 話, you have to choose an appropriate English word wisely depending on what it is actually referring to.