Unsupervised learning methods, such as Deep Image Prior (DIP), have shown great potential in tomographic imaging due to their training-data-free nature and high generalization capability. However, their reliance on numerous network parameter iterations results in high computational costs, limiting their practical application, particularly in complex 3D or time-sequence tomographic imaging tasks. To overcome these challenges, we propose Deep Dynamic Image Prior (D2IP), a novel framework for 3D time-sequence imaging. D2IP introduces three key strategies - Unsupervised Parameter Warm-Start (UPWS), Temporal Parameter Propagation (TPP), and a customized lightweight reconstruction backbone, 3D-FastResUNet - to accelerate convergence, enforce temporal coherence, and improve computational efficiency. Experimental results on both simulated and clinical pulmonary datasets demonstrate that D2IP enables fast and accurate 3D time-sequence Electrical Impedance Tomography (tsEIT) reconstruction. Compared to state-of-the-art baselines, D2IP delivers superior image quality, with a 24.8% increase in average MSSIM and an 8.1% reduction in ERR, alongside significantly reduced computational time (7.1x faster), highlighting its promise for clinical dynamic pulmonary imaging.