Gallium Nitride High Electron Mobility Transistors (GaN HEMTs) are promising devices for next-generation power electronic systems due to their high efficiency, high power density, and broad applicability in areas including electric vehicles, renewable energy, and communication. Existing studies on Prognostic and Health Management (PHM) of GaN HEMTs focus on the statistical behaviors of multiple devices under specific circumstances, which means individual device variability is neglected in these approaches. This work addresses the gap in individual health status by applying deep learning to achieve the Remaining Useful Lifetime (RUL) prediction of individual p-type GaN HEMT devices under diverse working conditions. In the proposed method, a Temporal Convolutional Network (TCN) integrated with attention mechanisms is developed to extract informative features and emphasize critical features within the measurements. To handle the varying lifetimes of p-GAN HEMT devices tested under different temperatures and stress voltages, we propose a prediction pipeline, which estimates the relative RUL in percentage and then converts it into absolute RUL in seconds. The Leave-One-Group-Out (LOGO) Cross-Validation (CV) is applied to ensure the generalization of the proposed method by testing the model on data collected from the unseen environment.