Transfer learning in reinforcement learning (RL) seeks to accelerate learning in new tasks by leveraging knowledge from related sources. Existing neurosymbolic transfer methods, however, typically rely on manually specified task automata, assume a single source task, and use fixed knowledge-integration mechanisms that cannot adapt to varying source relevance. We propose LANTERN, a unified framework for multi-source neurosymbolic transfer that addresses these limitations through three components: (i) deterministic finite automata generated from natural language task descriptions using large language models, (ii) semantic embedding-based aggregation of multiple source policies weighted by cross-task similarity, and (iii) adaptive teacher-student gating based on temporal-difference error and semantic uncertainty. Across domains spanning resource management, navigation, and control, LANTERN achieves 40-60% improvements in sample efficiency over existing baselines while remaining robust to poorly aligned sources. These results demonstrate that multi-source, adaptively weighted neurosymbolic transfer can improve scalability and robustness in symbolic RL settings.