Large Language Models (LLMs) face severe challenges in long-context processing, including quadratic computational costs, information forgetting, and the context fragmentation inherent in Retrieval-Augmented Generation (RAG). We introduce LycheeMemory, a cognitively inspired framework that enables efficient long-context inference via chunk-wise compression and selective memory recall, rather than processing all raw tokens. LycheeMemory segments the input into chunks and encodes each into compressed KV-cache style representations using a Compressor. A Gate then dynamically selects relevant memory blocks, which a Reasoner iteratively processes with an evolving working memory to solve downstream tasks. The Compressor and Reasoner are jointly optimized via end-to-end reinforcement learning, while the Gate is trained separately as a classifier. Experimental results demonstrate that LycheeMemory achieves competitive accuracy (up to 82% in ablation variants) on multi-hop reasoning benchmarks (e.g., RULER-HQA), successfully extrapolates context length from 7K to 1.75M, and provides a favorable accuracy–efficiency trade-off against strong long-context baselines. Notably, compared to MemAgent, LycheeMemory achieves an average 2× reduction in peak GPU memory usage and a 6× speedup during inference.