Large language models (LLMs) continue to struggle with low-resource languages, primarily due to limited training data, translation noise, and unstable cross-lingual alignment. To address these challenges, we propose LiRA (Linguistic Robust Anchoring for LLMs)-a plug-and-play framework that requires only lightweight fine-tuning on top of existing pretrained backbones. LiRA jointly optimizes representation stability and cross-lingual semantic consistency by combining two key components: Arca (Anchored Representation Composition Architecture), which aligns low-resource inputs to a shared English semantic space through anchor-based alignment and collaborative encoding; and LaSR (Language-coupled Semantic Reasoner), a lightweight, language-aware head that enforces consistency regularization for unified cross-lingual understanding, retrieval, and reasoning. We theoretically show that under controlled anchoring error and translation-induced bias, LiRA guarantees bounded representation deviation and stable downstream performance under local Lipschitz continuity. To facilitate research, we release a new multilingual product retrieval dataset covering five Southeast Asian and two South Asian languages. Extensive experiments across diverse low-resource benchmarks demonstrate consistent improvements in retrieval, ranking, question answering, and reasoning tasks. Code will be publicly available on GitHub, and the dataset will be hosted on Hugging Face.