A brand is worried about whether people remember their campaigns. Which metric within a Brand Lift study directly measures this?

Ad recall is the metric that measures this directly. In a Brand Lift study, ad recall asks whether people remember seeing the advertising, comparing responses from an exposed group with a control group that did not see it; the difference is the lift. It is the most immediate of the Brand Lift metrics because memory is the first thing an ad has to achieve — nothing further can happen if the audience does not remember the campaign at all. The others measure different stages of the same journey: awareness covers knowing the brand exists, consideration whether it is a candidate, favourability how people feel about it, and purchase intent whether they plan to buy. Frequency is not a Brand Lift metric at all, though it does influence recall, since too few exposures leave no impression and too many cause fatigue.