Three-dimensional Networks-on-Chip (3D-NoC) application mapping is a nondeterministic polynomial-time hard problem by nature. Under tight design restrictions, the efficient allocation of Intellectual Property (IP) cores to processing components must balance silicon area, reduce power consumption, and reduce end-to-end latency. To achieve improved mapping quality for 3D-NoC designs, this paper presents a Hybrid Lemur–Dwarf Mongoose Optimisation (LDMO) approach that addresses the cooperative exploitation abilities of Dwarf Mongoose Optimisation and the exploratory behaviour of Lemur Optimisation. To prevent premature stagnation, the Lemur Optimisation Algorithm mimics lemur cliff-leaping and tree-navigating behaviour during first stage. This produces a diversity of initial mapping candidates with high population variance. To optimise the mapping to global optima with high convergence speed, the Dwarf Mongoose Optimisation Algorithm employs adaptive leadership, sentinel–scout coordination, and foraging-based neighbourhood search during the second stage. The average communication delay (hop-dependent propagation, serialisation, and router latencies), area overhead (switch, interconnect, and core dimensions), and total power dissipation (router and interconnect power) are all minimised at the same time through a multi-objective fitness function. By adaptive switching between the two phases, the hybrid approach dynamically trades off between exploration and exploitation to ensure robustness across a wide range of communication demands and traffic patterns. Simulation outcomes demonstrate that the proposed LDMO framework consistently delivers reduced computation overhead, marked improvements in latency, and substantial energy efficiency. Furthermore, as the number of cores and communication links scale upward, the hybrid optimisation strategy maintains high-quality mapping solutions, underscoring its robust scalability across diverse NoC configurations.