Lexicon or dictionary generation across domains has the potential for societal impact, as it can potentially enhance information accessibility for a diverse user base while preserving language identity. Prior work in the field primarily focuses on bilingual lexical induction, which deals with word alignments using mapping-based or corpora-based approaches. However, these approaches do not cater to domain-specific lexicon generation that consists of domain-specific terminology. This task becomes particularly important in specialized medical, engineering, and other technical domains, owing to the highly infrequent usage of the terms and scarcity of data involving domain-specific terms especially for low-resource languages. We propose a new model to generate dictionary words for 6 Indian languages in the multi-domain setting. Our model consists of domain-specific and domain-generic layers that encode information, and these layers are invoked via a learnable routing technique. We also release a new benchmark dataset consisting of >75K translation pairs across 6 Indian languages spanning 8 diverse domains. We conduct both zero-shot and few-shot experiments across multiple domains to show the efficacy of our proposed model in generalizing to unseen domains and unseen languages. Additionally, we also perform a human post-hoc evaluation on unseen languages. The source code and dataset is present at https://github.com/Atulkmrsingh/lexgen.