To connect Jhumpa Lahiri's works with cultural studies, you can focus on the themes of cultural identity and the immigrant experience that are prevalent in her writing. Lahiri's work often explores the experiences of Indian immigrants in America, and the ways in which their culture and traditions intersect with and shape their lives in a new and unfamiliar environment. Through her writing, Lahiri sheds light on the complexities of the immigrant experience, including issues of adaptation, assimilation, and intergenerational conflict.
There is also an option to have a look at Lahiri's texts from the perspective of quantitative linguistics, which enable researchers to study semantic intricacies intersubjectively. If you wish, feel free to contact me for further information.