This article explores the integration of a relay station with two intelligent reflecting surfaces (IRSs) to enhance energy efficiency (EE) and system throughput (ST) in low-power wide-area networks (LPWAN) modelled for Internet of Things (IoT) applications. By leveraging IRS technology, the system improves communication between IoT sensors, the relay station, and the IoT gateway, mitigating signal degradation and optimizing energy consumption. To demonstrate these improvements, we derive theoretical expressions for ST and EE in an LPWAN environment, considering IRS-assisted relay transmission over Nakagami-m fading channels. Our analysis demonstrates that incorporating IRSs leads to significant performance enhancements compared to conventional non-IRS systems. More specifically, the proposed network achieves a power reduction of 10 dBm while achieving the same ST and EE targets, highlighting its energy efficiency advantages. Furthermore, our results show that an LPWAN employing a relay station and IRSs is capable of maintaining reliable operation in high-frequency regimes, such as 5 GHz, while maintaining stable communication over distances of up to 200 meters. We conduct an in-depth investigation into the impact of various factors, including the number of reflecting elements, IRS placement, data transmission rate, available bandwidth, and operating frequency, on overall system performance. These insights provide valuable guidelines for the future design and deployment of IRS-assisted IoT frameworks, ensuring efficient, high-performance communication in LPWAN environments.