Low-Altitude Economy Networks (LAENets) are emerging as a promising paradigm to support various low-altitude services through integrated air-ground infrastructure. To satisfy low-latency and high-computation demands, the integration of Unmanned Aerial Vehicles (UAVs) with Mobile Edge Computing (MEC) systems plays a vital role, which offloads computing tasks from terminal devices to nearby UAVs, enabling flexible and resilient service provisions for ground users. To promote the development of LAENets, it is significant to achieve low-carbon multi-UAV-assisted MEC networks. However, several challenges hinder this implementation, including the complexity of multi-dimensional UAV modeling and the difficulty of multi-objective coupled optimization. To this end, this paper proposes a novel Retrieval Augmented Generation (RAG)-based Large Language Model (LLM) agent framework for model formulation. Specifically, we develop HybridRAG by combining KeywordRAG, VectorRAG, and GraphRAG, empowering LLM agents to efficiently retrieve structural information from expert databases and generate more accurate optimization problems compared with traditional RAG-based LLM agents. After customizing carbon emission optimization problems for multi-UAV-assisted MEC networks, we propose a Double Regularization Diffusion-enhanced Soft Actor-Critic (R\textsuperscript{2}DSAC) algorithm to solve the formulated multi-objective optimization problem. The R\textsuperscript{2}DSAC algorithm incorporates diffusion entropy regularization and action entropy regularization to improve the performance of the diffusion policy. Furthermore, we dynamically mask unimportant neurons in the actor network to reduce the carbon emissions associated with model training. Simulation results demonstrate the effectiveness and reliability of the proposed HybridRAG-based LLM agent framework and the R\textsuperscript{2}DSAC algorithm.