Generative Face Video Coding (GFVC) achieves superior rate-distortion performance by leveraging the strong inference capabilities of deep generative models. However, its practical deployment is hindered by large model parameters and high computational costs. To address this, we propose a lightweight GFVC framework that introduces dual-mode optimization -- combining architectural redesign and operational refinement -- to reduce complexity whilst preserving reconstruction quality. Architecturally, we replace traditional 3 x 3 convolutions with slimmer and more efficient layers, reducing complexity without compromising feature expressiveness. Operationally, we develop a two-stage adaptive channel pruning strategy: (1) soft pruning during training identifies redundant channels via learnable thresholds, and (2) hard pruning permanently eliminates these channels post-training using a derived mask. This dual-phase approach ensures both training stability and inference efficiency. Experimental results demonstrate that the proposed lightweight dual-mode optimization for GFVC can achieve 90.4% parameter reduction and 88.9% computation saving compared to the baseline, whilst achieving superior performance compared to state-of-the-art video coding standard Versatile Video Coding (VVC) in terms of perceptual-level quality metrics. As such, the proposed method is expected to enable efficient GFVC deployment in resource-constrained environments such as mobile edge devices.