Immediate thoughts, before reading comments: One-box. I had started to think more deeply until I read the part about being run over for factoring, and for some reason my brain applied it to reasoning about this topic as a whole and spit out a final answer.

Intuitively, it seemed one boxing would get me a million, as per standard Newcomb. The lottery two million seemed like gravy above that (diminishing marginal utility of money), with a potential for 3 million total. Since they're independent, the word "separately" and its description made it seem like the lottery was unable to be affected by my actions at all. Thus, take box B, and hope for a lottery win. Definitely don't over think it, or risk a trolley encounter.