Early on in Star Trek: Discovery, we don’t see any outward signs of Landry’s romance with Lorca, but we do see plenty of her outright antagonism toward others, especially Burnham. We meet Landry when Burnham does, and that’s when the security officer refers to the other woman and her fellow prisoners as “garbage.” Landry obviously hates Starfleet’s first mutineer on sight, but it’s notable that she sees these prisoners as garbage to be processed rather than lives to be rehabilitated.
Her antipathy towards Burnham continues later on as she critiques the other woman’s Vulcan martial arts techniques. Most interestingly, Landry mentions how she and Burnham need to find “poison sacs, pain inducers, rage glands” on their captured tardigrade. When an understandably concerned Burnham talks about how weird it is to look at a new life-form like this, Landry lectures her on how Captain Lorca is only “interested in what you can do for him…And if he needs us to make that thing useful in his war effort, that’s what we’re gonna do.”