Radio Frequency Interference (RFI) from anthropogenic radio sources poses significant challenges to current and future radio telescopes. Contemporary approaches to detecting RFI treat the task as a semantic segmentation problem on radio telescope spectrograms. Typically, complex heuristic algorithms handle this task of `flagging' in combination with manual labeling (in the most difficult cases). While recent machine-learning approaches have demonstrated high accuracy, they often fail to meet the stringent operational requirements of modern radio observatories. Owing to their inherently time-varying nature, spiking neural networks (SNNs) are a promising alternative method to RFI-detection by utilizing the time-varying nature of the spectrographic source data. In this work, we apply Liquid State Machines (LSMs), a class of spiking neural networks, to RFI-detection. We employ second-order Leaky Integrate-and-Fire (LiF) neurons, marking the first use of this architecture and neuron type for RFI-detection. We test three encoding methods and three increasingly complex readout layers, including a transformer decoder head, providing a hybrid of SNN and ANN techniques. Our methods extend LSMs beyond conventional classification tasks to fine-grained spatio-temporal segmentation. We train LSMs on simulated data derived from the Hyrogen Epoch of Reionization Array (HERA), a known benchmark for RFI-detection. Our model achieves a per-pixel accuracy of 98% and an F1-score of 0.743, demonstrating competitive performance on this highly challenging task. This work expands the sophistication of SNN techniques and architectures applied to RFI-detection, and highlights the effectiveness of LSMs in handling fine-grained, complex, spatio-temporal signal-processing tasks.