LLM inference serving typically scales out with a two-tier architecture: a cluster router distributes requests to multiple inference engines, each of which then in turn performs its own internal scheduling. However, this commonly used paradigm suffers from critical, systemic inefficiency caused by the information gaps across two layers. At the cluster-layer, the router mainly relies on lagging, coarse-grained metrics, such as average latency and queue length to make decisions, resulting in "decision lag" that leads to suboptimal request routing. At the engine-layer, static heuristic scheduling policies cannot effectively handle the dynamic workloads, leading a poor balance between latency and throughput. Besides, these gaps may cause SLO violations and resource waste, especially in heterogeneous cloud environments. To bridge such gaps, we propose NexusSched, a cross-layer framework that shifts LLM serving system from reactive load balancing to predictive orchestration. The core of NexusSched lies in a structurally-informed online performance model that provides accurate, forward-looking per-step latency and capacity estimations. This model empowers two key components. At the engine-layer, LENS performs SLO-aware, adaptive scheduling, dynamically optimizing batching to meet SLOs under real-time loads. At the cluster-layer, PRISM uses predictive signals to perform state-driven routing, maximizing cluster-wide performance and SLO attainment. Performance evaluations show that NexusSched improves SLO attainment by 43% on average and achieves up to 3x throughput speedup in long-context and heterogeneous scenarios. Besides, we also deploy NexusSched on FlowGPT's clusters to demonstrate its advantages in production environment.