Cross-lingual alignment of nuanced sociological concepts is crucial for comparative cross-cultural research, harmonising longitudinal studies, and leveraging knowledge from social science taxonomies (e.g., ELSST). However, aligning these concepts is challenging due to cultural context-dependency, linguistic variation, and data scarcity, particularly for low-resource languages. Existing methods often fail to capture domain-specific subtleties or require extensive parallel data. Grounded in a Vector Decomposition Hypothesis—positing separable domain and language components within embeddings, supported by observed language-pair specific geometric structures—we propose DLIR (Dual-Branch LoRA for Invariant Representation). DLIR employs parallel Low-Rank Adaptation (LoRA) branches: one captures core sociological semantics (trained primarily on English data structured by the ELSST hierarchy), while the other learns language invariance by counteracting specific language perturbations. These perturbations are modeled by Gaussian Mixture Models (GMMs) fitted on minimal parallel concept data using spherical geometry. DLIR significantly outperforms strong baselines on cross-lingual sociological concept retrieval across 10 languages. Demonstrating powerful zero-shot knowledge transfer, English-trained DLIR substantially surpasses target-language (French/German) LoRA fine-tuning even in monolingual tasks. DLIR learns disentangled, language-robust representations, advancing resource-efficient multilingual understanding and enabling reliable cross-lingual comparison of sociological constructs.