The lecture on Sophocles' 'Oedipus Rex' explores the tragic story of Oedipus, who unwittingly kills his father and marries his mother, leading to his downfall amidst themes of free will, self-discovery, pride, and fate. Oedipus's journey to uncover the truth about his origins results in severe consequences, including the suicides and punishments that ultimately restore order to Thebes. The play highlights the complexities of fate and the implications of human choices, emphasizing the relationship between character and destiny.