Modern Retrieval-Augmented Generation (RAG) systems struggle with a fundamental architectural tension: vector indices are optimized for query latency but poorly handle continuous knowledge updates, while data lakes excel at versioning but introduce query latency penalties. We introduce LiveVectorLake, a dual-tier temporal knowledge base architecture that enables real-time semantic search on current knowledge while maintaining complete version history for compliance, auditability, and point-in-time retrieval. The system introduces three core architectural contributions: (1) Content-addressable chunk-level synchronization using SHA-256 hashing for deterministic change detection without external state tracking; (2) Dual-tier storage separating hot-tier vector indices (Milvus with HNSW) from cold-tier columnar versioning (Delta Lake with Parquet), optimizing query latency and storage cost independently; (3) Temporal query routing enabling point-in-time knowledge retrieval via delta-versioning with ACID consistency across tiers. Evaluation on a 100-document corpus versioned across five time points demonstrates: (i) 10-15% re-processing of content during updates compared to 100% for full re-indexing; (ii) sub-100ms retrieval latency on current knowledge; (iii) sub-2s latency for temporal queries across version history; and (iv) storage cost optimization through hot/cold tier separation (only current chunks in expensive vector indices). The approach enables production RAG deployments requiring simultaneous optimization for query performance, update efficiency, and regulatory compliance. Code and resources: [https://github.com/praj-tarun/LiveVectorLake]