The idea of a lottery represents a level of reality that transcends not only intellect but even will. This is the level of G-dliness known as "Ba'al HaRatzon" which means the master of the will. On that level, atonement for violation of G-d's will is possible. After understanding this, however, we are left with the question why Haman would have attempted to invoke such a concept that facilitates atonement for the Jewish people. The answer is that within the system of creation, Haman knew that he could not defeat the Jews. However, if he could access the level of randomness, there was at least a possibility that his plan would succeed.

Chapters 3-5 of the discourse.