Generative reasoning with large language models (LLMs) often involves long decoding sequences, leading to substantial memory and latency overheads from accumulating key-value (KV) caches. While existing KV compression methods primarily focus on reducing prefill memory from long input sequences, they fall short in addressing the dynamic and layer-sensitive nature of long-form generation, which is central to reasoning tasks. We propose Lethe, a dynamic KV cache management framework that introduces adaptivity along both the spatial and temporal dimensions of decoding. Along the spatial dimension, Lethe performs layerwise sparsity-aware allocation, assigning token pruning budgets to each transformer layer based on estimated attention redundancy. Along the temporal dimension, Lethe conducts multi-round token pruning during generation, driven by a Recency-Aware Selective Retention (RASR) mechanism. RASR extends traditional recency-based heuristics by also considering token relevance derived from evolving attention patterns, enabling informed decisions about which tokens to retain or evict. Empirical results demonstrate that Lethe achieves a favorable balance between efficiency and generation quality across diverse models and tasks, increases throughput by up to 2.56×.