LLMs are increasingly executed in edge where limited GPU memory and heterogeneous computation jointly constrain deployment which motivates model partitioning and request scheduling. In this setting, minimizing latency requires addressing the tight coupling between model placement and request scheduling across heterogeneous nodes, as suboptimal decisions in one domain can negate benefits in the other. In this paper, we propose Hyperion, a hierarchical two-stage framework that jointly optimizes partitioning and scheduling for pipelined LLM inference. Hyperion minimizes latency by balancing resources across tiers without requiring model retraining or incurring significant runtime overhead. Leveraging the timescale difference between partitioning and request arrivals, Stage 1 performs offline, inter-tier partitioning via a Hyperion Split with Dynamic Programming (HypSplit-DP) procedure to produce balanced stage times under tier capacity and memory constraints; to adapt to time-varying load, Stage 2 performs online, intra-tier scheduling with a lightweight Hyperion Scheduling for Real-Time (HypSched-RT) that maps each request to the best available node using real-time estimates of queue length and effective capacity. Experiments with Phi-3-medium demonstrate that Hyperion reduces latency by up to 52.1% (vs. GPipe) and 31.2% (vs. HEFT). Furthermore, Hyperion exhibits superior scalability for long-sequence generation, maintaining 44.5% lower latency and higher GPU utilization.