We propose SALT (Split-Adaptive Lightweight Tuning), a lightweight model adaptation framework for Split Computing under closed constraints, where the head and tail networks are proprietary and inaccessible to users. In such closed environments, conventional adaptation methods are infeasible since they require access to model parameters or architectures. SALT addresses this challenge by introducing a compact, trainable adapter on the client side to refine latent features from the head network, enabling user-specific adaptation without modifying the original models or increasing communication overhead. We evaluate SALT on user-specific classification tasks with CIFAR-10 and CIFAR-100, demonstrating improved accuracy with lower training latency compared to fine-tuning methods. Furthermore, SALT facilitates model adaptation for robust inference over lossy networks, a common challenge in edge-cloud environments. With minimal deployment overhead, SALT offers a practical solution for personalized inference in edge AI systems under strict system constraints.