Learning Management Systems (LMS) have become central to the digital learning experience. But providing timely and reliable technical support remains a challenge for universities with large communities. Students and lecturers frequently encounter technical issues such as login failures, course enrolment errors, broken content links and difficulties with online assessments. All of which place heavy demands on human helpdesks. Traditional solutions such as static FAQ pages or scripted chatbots are often unable to keep pace with the scale and variety of queries. In this context, generative artificial intelligence (AI) offers a promising alternative. This paper presents a comprehensive framework for integrating generative AI into LMS technical support using a Design Science Research (DSR) approach and validated through an institutional case. By combining Retrieval-Augmented Generation (RAG) with conversational models like ChatGPT, the framework delivers context‑aware and source‑grounded answers. It operates seamlessly across multiple platforms, including web widgets and WhatsApp. The architecture is designed with layered guardrails, fallback mechanisms and evaluation loops to ensure accuracy, transparency and trustworthiness. Findings indicate that generative AI chatbots can reduce response times, ease the burden on human staff and improve user satisfaction when deployed responsibly. The contribution is not a one-size-fits-all tool but a structured, adaptable approach that higher education institutions can tailor to their contexts. This study shows how generative AI can be integrated into LMS technical support through a structured framework that reduces response times, eases the burden on helpdesks and improves user satisfaction while ensuring accuracy and trust.