Salicylates cause lactic acidosis by interfering with the enzymes of Krebs cycle.
Specifically, alpha-ketoglutarate dehydrogenase and succinic acid dehydrogenase appear to be targets.
Obviously this sort of uncoupling would lead to increased anaerobic metabolism, and therefore lactate levels would rise.
However, it seems clinically that the lactate levels in these people rise only infrequently, which makes salicylates an unusual cause of lactic acidosis. The lactate may be slightly elevated, but does little to contribute to the overall acidosis picture.