To address the computational challenges in modeling laser-produced plasma spatiotemporal evolution, this study pioneers the application of neural operators for 2D radiation hydrodynamics (RHD) simulations in fiber-laser-produced plasma systems employing liquid tin droplets for extreme ultraviolet lithography (EUVL) sources. Our novel framework enables rapid prediction of multi-physics field evolution by learning the underlying physical operators governing the complex interplay between radiation transport, hydrodynamic motion and plasma dynamics in EUV light source configurations. Through comparative analysis with convolutional long short-term memory (ConvLSTM) and convolutional neural operator (CNO) architectures, using over 50,000 spatiotemporal snapshots generated by FLASH software, the multi-variable Fourier neural operator (FNO) demonstrates superior performance in all three cases. In the case of single-laser pulse scenarios, it achieves an electron density mean squared error (MSE) of 7.49×10⁻⁵, representing a 53% improvement over ConvLSTM (1.58×10⁻⁴) and a 50% improvement over the CNO (1.51×10⁻⁴) in the normalized domain. The FNO exhibits unique zero-shot super-resolution capabilities, reconstructing high-fidelity 96×192 grid solutions from low-resolution 48×96 inputs while maintaining a normalized MSE of 10⁻⁴ relative to ground truth simulations. Demonstrating six-order-of-magnitude acceleration compared to conventional RHD solvers, this approach enables real-time analysis of plasma evolution patterns critical for EUVL source optimization, including tin droplet fragmentation dynamics and extreme ultraviolet emission characteristics. The demonstrated multi-physics modeling capability and memory-efficient super-resolution reconstruction positions FNO as a potential transformative tool for next-generation plasma diagnostics and EUVL system monitoring.