Large language models (LLMs) rely on Key-Value (KV) cache to reduce time-to-first-token (TTFT) latency, but existing disk-based KV cache systems using file-per-object layouts suffer from severe scalability bottlenecks due to file system metadata overhead, I/O inefficiency, and poor spatial locality. This paper presents SGLANG-LSM, a database-inspired system that leverages Log-Structured Merge-tree (LSM-tree) architectures for scalable KV cache management. SGLANG-LSM implements a layered system design with three coordinated components: (1) a prefix-preserving storage engine that maintains token sequence locality while efficiently storing large KV cache tensors through key-value separation, (2) an adaptive controller that dynamically optimizes LSM-tree configurations based on shifting workload characteristics, and (3) runtime services including batch operations and automatic resource management for production deployment. Evaluation on large-scale dynamic workloads demonstrates that SGLANG-LSM significantly improves cache hits by up to 143% and reduces TTFT by up to 24% compared to state-of-the-art systems, representing the first systematic application of database storage architectures to large-scale LLM cache management.