This paper proposes a Low Earth Orbit (LEO) Positioning, Navigation, and Timing (PNT) system leveraging LoRaWAN signals. We introduce a framework for processing LoRa transmissions in LEO scenarios, featuring a robust method for Doppler shift and time-delay estimation. To address collision-induced performance degradation caused by the ALOHA-based medium access protocol, we present an interference mitigation strategy. The system is evaluated through extensive Monte Carlo simulations, demonstrating reliable performance in single-signal conditions. Results indicate robust time-delay and Doppler estimations under collision. However, the data demodulation before decoding is slightly compromised. A proof-of-concept experiment with real signals has also been conducted. This work provides foundational insights into LoRaWAN-based LEO PNT systems and their challenges in practical deployments.