Abstract Lexical entailment (LE; also known as hyponymy-hypernymy or is-a relation) is a core asymmetric lexical relation that supports tasks like taxonomy induction and text generation. In this work, we propose a simple and effective method for fine-tuning distributional word vectors for LE. Our Generalized Lexical ENtailment model (GLEN) is decoupled from the word embedding model and applicable to any distributional vector space. Yet – unlike existing retrofitting models – it captures a general specialization function allowing for LE-tuning of the entire distributional space and not only the vectors of words seen in lexical constraints. Coupled with a multilingual embedding space, GLEN seamlessly enables cross-lingual LE detection. We demonstrate the effectiveness of GLEN in graded LE and report large improvements (over 20% in accuracy) over state-ofthe-art in cross-lingual LE detection