Taxonomies are hierarchical knowledge graphs crucial for recommendation systems, and web applications. As data grows, expanding taxonomies is essential, but existing methods face key challenges: (1) discriminative models struggle with representation limits and generalization, while (2) generative methods either process all candidates at once, introducing noise and exceeding context limits, or discard relevant entities by selecting noisy candidates. We propose LORex (Lineage-Oriented Reasoning for Taxonomy Expansion), a plug-and-play framework that combines discriminative ranking and generative reasoning for efficient taxonomy expansion. Unlike prior methods, LORex ranks and chunks candidate terms into batches, filtering noise and iteratively refining selections by reasoning candidates' hierarchy to ensure contextual efficiency. Extensive experiments across four benchmarks and twelve baselines show that LORex improves accuracy by 12% and Wu & Palmer similarity by 5% over state-of-the-art methods.