As an emerging technology, digital twin (DT) can provide real-time status and dynamic topology mapping for Internet of Things (IoT) devices. However, DT and its implementation within industrial IoT networks necessitates substantial, distributed data support, which often leads to ``data silos'' and raises privacy concerns. To address these issues, we develop a dynamic resource scheduling algorithm tailored for the asynchronous federated learning (FL)-based lightweight DT empowered IoT network. Specifically, our approach aims to minimize a multi-objective function that encompasses both energy consumption and latency by optimizing IoT device selection and transmit power control, subject to FL model performance constraints. We utilize the Lyapunov method to decouple the formulated problem into a series of one-slot optimization problems and develop a two-stage optimization algorithm to achieve the optimal transmission power control and IoT device scheduling strategies. In the first stage, we derive closed-form solutions for optimal transmit power on the IoT device side. In the second stage, since partial state information is unknown, e.g., the transmitting power and computational frequency of IoT device, the edge server employs a multi-armed bandit (MAB) framework to model the IoT device selection problem and utilizes an efficient online algorithm, namely the client utility-based upper confidence bound (CU-UCB), to address it. Numerical results validate our algorithm's superiority over benchmark schemes, and simulations demonstrate that our algorithm achieves faster training speeds on the Fashion-MNIST and CIFAR-10 datasets within the same training duration.