This paper presents a novel architecture for integrating Large Language Models (LLMs) with Retrieval-Augmented Generation (RAG) into Learning Management Systems (LMS), resulting in a contextualized AI-driven Learning Assistance (AILA) that delivers personalized, real-time learning support. Leveraging a middleware approach, the system securely orchestrates relevant data, such as Learning Object Metadata (LOM) and course materials, into a modular RAG pipeline. The chatbot combines quality-assured question answering and document-grounded responses, using advanced retrieval techniques, including re-ranking and relevance filtering. A real-world evaluation in a hybrid training program demonstrated meaningful improvements in learning outcomes and strong user acceptance, validating both its pedagogical impact and technical reliability. These results highlight the potential of open-source AILA systems to enhance digital learning environments and support the development of responsive, learner-centered educational technologies.