Lane changing entails simultaneous longitudinal and lateral motions that affect driving comfort and mobility efficiency. Because these motions are tightly coupled and subject to substantial inter-vehicle variability, trajectory planning for lane-change maneuvers is characterized by a highly personalized nature. This study proposes a neural network-driven planner that integrates a third-order polynomial trajectory generator with a learning module that infers optimal trajectory parameters across diverse driving conditions. Using a shared backbone with dual heads, one head ensures all-condition operational guarantees, while the other captures driver-specific preferences for comfort or mobility efficiency. A head-gated switching mechanism, realized through a statistical gate based on error-winner logistic regression, adaptively selects the appropriate head under varying driving conditions, which enables context-aware lane-change trajectory planning. Representative cases and Monte Carlo simulations show that the proposed planner achieves personalized comfort and mobility during lane changes, while the baseline ensures feasible trajectories under driving conditions where personalized data are insufficient or inaccessible.