Recent progress in large language model (LLM) based generative recommendation (GR) shows that leveraging LLM world knowledge can substantially improve performance. However, existing methods rely on fixed, manually designed instructions to generate semantic knowledge and directly incorporate it into GR, which has two limitations: (1) fixed instructions cannot capture the multidimensional heterogeneity of user interests; (2) uncontrollable knowledge fusion may conflict with behavioral signals and harm recommendations. To address these limitations, we propose LWGR, a framework that leverages Lagrangian constraints to transfer users' personalized World knowledge from LLMs into Generative Recommendation. LWGR enhances GR along two axes: knowledge extraction and fusion. It builds user personalized soft instructions to extract behavior-relevant LLM world knowledge. Then, it formulates knowledge fusion as an optimization problem with explicitly bounded performance degradation, solved via a Lagrangian primal–dual method that selectively incorporates beneficial knowledge. We further design two training strategies for different LLM scales and a deployment scheme that combines nearline precomputation with lightweight online serving. Experiments on multiple public datasets and one industrial dataset show that LWGR outperforms eight state-of-the-art baselines by up to 11.23% and brings a 1.35% revenue lift on a large-scale advertising platform, demonstrating its effectiveness and practicality.