The Smoking Lesion is a needlessly confusing Newcomblike problem to probe the stances of alternative decision theories. If you want an equivalent problem that is not needlessly confusing, see the Toxoplasmosis dilemma.
Smoking Lesion is stated as:
Smoking is strongly correlated with lung cancer, but in the world of the Smoker's Lesion this correlation is understood to be the result of a common cause: a genetic lesion that tends to cause both smoking and cancer. Once we fix the presence or absence of the lesion, there is no additional correlation between smoking and cancer.
Suppose you prefer smoking without cancer to not smoking without cancer, and prefer smoking with cancer to not smoking with cancer. Should you smoke?
(Again, note that contrary to how causality works in the real world, this example wantonly inverts the real world to say: "Actually smoking does not cause cancer; instead, enjoyment of smoking is correlated with a genetic cause for cancer"; except that instead of just calling it a gene, they're going to call it a "lesion" that you might otherwise associate with a brain lesion or something. This is why the statement is needlessly confusing and why presentations should perhaps use some less confusing presentation like Toxoplasmosis instead.)
Once you've got those needlessly confusing specifications straight in your mind, perhaps after first looking at Toxoplasmosis to understand what the idea is actually about:
Causal decision theory says "yes" to smoking in Smoking Lesion, since smoking in this world has no causal effect on whether or not you get cancer. You either get cancer or not; in both cases, smoking is preferred.
(Naive) evidential decision theory says "no", because smoking is strongly correlated with cancer.
Functional Decision Theory says "yes": your decision procedure in this problem doesn't influence whether or not you get cancer; and with or without cancer, smoking is preferred.