A “lit review” or a literature review or a review of the literature is the section of a research paper that provides an overview of the state of the research on the topic of the paper. This is where one would explore all the empirical evidence for what “is” with the issue.
A theory section is where one traces out an explanation to explain why a particular relationship exists or why a trend is occurring. A theory section is sometime explicitly stated in a paper and sometimes is implicitly included at the end of a literature review. Generally speaking a lit review is the “what” and the theory section is the “why.”
An example might be that if I were writing a paper about the impact of breastfeeding on women’s earnings, in the literature review I would detail all the research showing what we know about this, such as that women who breastfeed for longer durations experience steeper earnings trajectories than do women who breastfeed for shorter durations or not at all (Rippeyoung and Noonan 2012). In the theory section, I would explain why this is and I might offer multiple theories at different levels. At the middle level of theory, I might simply argue that women who breastfeed are going to work fewer hours per week given few structural supports in the workplace to facilitate breastfeeding. At a grand level of theory, I might argue that our social structure is defined by male supremacy that means that women’s bodies are not welcome in the public sphere unless they conform to male bodies. Note that the former theory is much easier to test with data, although that latter could be just as “true.” The ease of testing often explains why we see less grand theory in empirical research since finding measures of things like “male supremacy” are much harder than things like “work hours.”