Here are two links to overviews of Macrobiotics that mention Leukemia. Neither are specifically about Chronic Lymphocytic Leukemia but they provide both the big picture and some details.
The Macrobiotic Diet by Ross Pelton & Lee Overholser: http://curezone.org/faq/q.asp?a=92,622&q=56
I haven’t read their book, Alternatives In Cancer Therapy, but I like this excerpt. Leukemia is yin, therefore; it is necessary to become more yang.
The Theory and Practice of the Dietary Component of Macrobiotics and its Role in Cancer Therapy by Michio Kushi: http://www.michiokushi.org/michio/speech010301.htm
He briefly summarizes the dietary cause of Leukemia as an “Over-consumption of refined sugar products, such as sugar, cakes, chocolate, and fruits and fruit juices; combined with oily/greasy foods.”