Timely information delivery in low-altitude networks is critical for many time-sensitive applications, such as unmanned aerial vehicle (UAV) navigation, inspection, and surveillance. The key challenge lies in balancing three competing factors: stringent data freshness requirements, UAV onboard energy consumption, and interference with terrestrial services. Addressing this challenge requires not only efficient power and channel allocation strategies but also effective communication timing over the entire operation horizon. In this work, we propose a model predictive communication (MPComm) framework, enabled by advanced channel sensing techniques, in which the channel conditions that the UAV will experience are largely predictable. Within this framework, we formulate a constrained bi-objective optimization problem to achieve a desired trade-off between energy consumption and terrestrial channel occupation, subject to a strict timeliness constraint. We solve this problem using Pareto analysis and show that the original non-convex, mixed-integer problem can be decomposed into a two-layer structure: the outer layer determines the optimal communication timing, while the inner layer determines the optimal power and channel allocation for each communication interval. An efficient algorithm for the inner problem is developed using non-convex analysis, with asymptotic optimality guarantees, while the outer problem is solved optimally via a simple graph search, with edges characterized by inner solutions. The proposed approach applies to a broad class of problem variants, including objective transformations and single-objective specializations. Numerical results demonstrate the efficiency of the proposed solution, achieving up to a six-fold reduction in terrestrial channel occupation and a 6dB energy saving compared to benchmark schemes.