Large language models (LLMs) are widely used in applications like conversation and text summarization. With the demand for model customization and privacy, lightweight fine-tuning methods for large models have begun to receive widespread attention. Low-Rank Adaption (LoRA) is one of the most widely used fine-tuning algorithms, which significantly reduces the tunable weights and associated optimizer memory when transferring pre-trained LLMs to downstream tasks. However, past works lacked attention to the overhead of buffered activations in low-rank adaption, leading to suboptimal system memory usage.To reduce buffered activation memory consumption and further enable the on-device memory efficient fine-tuning system, we propose \textbf{HyC-LoRA}, a variant of the LoRA training system using a hybrid compression framework enabling almost 2-bit buffered activation quantization in all operators. HyC-LoRA observes that the temporarily buffered activation for back-propagation dominates the memory consumption in the LoRA fine-tuning process, and those in non-linear modules act as dominant memory consumers, whose quantization is more challenging. Based on this, HyC-LoRA proposes a hybrid compression mechanism with two tiers: (1) \textit{\textbf{Intra-operator hybrid compression}}: HyC-LoRA detects extreme outliers in buffered activation and mitigates the quantization error by structured outlier storage; (2) \textit{\textbf{Inter-operator hybrid compression}}: HyC-LoRA utilizes the LoRA adapter to achieve compensation for quantization errors and selective recomputation, through inter-operator reordering and fusion. Finally, HyC-LoRA implements a buffered activation compression system and integrates it with the existing machine learning framework to complete the last mile of lightweight storage for fine-tuning algorithms. Evaluations with multiple LLMs such as Llama series, in widely-used downstream tasks show the proposed HyC-LoRA framework achieves up to 3.97× end-to-end memory reduction compared to baseline, with negligible accuracy degradation.