Current approaches to incorporating terminology constraints in machine translation (MT) typically assume that the constraint terms are provided in their correct morphological forms. This limits their application to real-world scenarios where constraint terms are provided as lemmas. In this paper, we introduce a modular framework for incorporating lemma constraints in neural MT (NMT) in which linguistic knowledge and diverse types of NMT models can be flexibly applied. It is based on a novel cross-lingual inflection module that inflects the target lemma constraints based on the source context. We explore linguistically motivated rule-based and data-driven neural-based inflection modules and design English-German health and English-Lithuanian news test suites to evaluate them in domain adaptation and low-resource MT settings. Results show that our rule-based inflection module helps NMT models incorporate lemma constraints more accurately than a neural module and outperforms the existing end-to-end approach with lower training costs.