Low-Power Wide-Area Network (LPWAN) technologies, such as LoRa, have gained significant attention for their ability to enable long-range, low-power communication for Internet of Things (IoT) applications. However, the security of LoRa networks remains a major concern, particularly in scenarios where device identification and classification of legitimate and spoofed signals are crucial. This paper studies a deep learning framework to address these challenges, considering LoRa device identification and legitimate vs. rogue LoRa device classification tasks. A deep neural network (DNN), either a convolutional neural network (CNN) or feedforward neural network (FNN), is trained for each task by utilizing real experimental I/Q data for LoRa signals, while rogue signals are generated by using kernel density estimation (KDE) of received signals by rogue devices. Fast Gradient Sign Method (FGSM)-based adversarial attacks are considered for LoRa signal classification tasks using deep learning models. The impact of these attacks is assessed on the performance of two tasks, namely device identification and legitimate vs. rogue device classification, by utilizing separate or common perturbations against these signal classification tasks. Results presented in this paper quantify the level of transferability of adversarial attacks on different LoRa signal classification tasks as a major vulnerability and highlight the need to make IoT applications robust to adversarial attacks.