The LAT wants you to provide arguments that are 1) well expressed and 2) logical. Being good at English Advanced or Modern History is an okay predictor of LAT success insofar as it correlates with having good written expression (e.g. sophisticated vocabulary, good grammar, varied sentence structure, etc.). These subjects aren't as good at predicting whether someone can think logically as a lot of the 'arguments' you pose in them are simply recitations of learned content.
In my view, the single best predictor of LAT success is being good at debating (the formal competition kind). Good competitive debaters know what the essential components of an argument are. This means they can both evaluate the validity of an argument (Q1) and propose logically coherent arguments of their own (Q2). They are also usually eloquent enough to be able to express these ideas in a clear and concise fashion.
