There exists an inherent profound contradiction between the particularity of ethnocultural cognition in lexical encoding and the shared cultural cognition required for multicultural interaction. The contradiction is deeply seated in linguistic underpinnings for the frequent misunderstandings and conflicts in cross-cultural communication. This paper proposes the L-C-U Model for Lexical Cultural Cognition and advocates that relevant research is expected to be carried out systematically from linguistic, conceptual and usage-based levels. Within the model, it discusses in detail seemingly corresponding English-Chinese word pair private and 私 (sī). There are three main findings presented as follows: (1) The etymological and semantic evolution of private demonstrates a narrative of continuous empowerment centered on individual tension, whereas 私 exhibits a discontinuous moral reconstruction of individual cultural cognition; (2) The cultural concept of private highlights exclusive ownership and control, while 私 has undergone a shift from neutral connotations of property rights to moral stigmatization; (3) The shared meanings of private and 私 are prone to misunderstanding in cross-cultural communication, stemming from their cultural conceptions they activate. Furthermore, a cognitive typological distinction between “container schema” and “relational schema” is put forward: English speakers conceptualize the individual as a closed container with clear boundaries, whereas Chinese speakers perceive the individual as a relational node with fluid boundaries. This study provides an operable analytical model for cultural cognitive linguistics and practical implications for such fields as international communication, foreign language lexical education and lexicography, and is of great significance for enhancing the international understanding of Chinese discourse and promoting exchanges and mutual learning among civilizations.