Light-field fluorescence microscopy (LFM) is a powerful elegant compact method for long-term high-speed imaging of complex biological systems, such as neuron activities and rapid movements of organelles. LFM experiments typically generate terabytes of image data and require a substantial amount of storage space. Some lossy compression algorithms have been proposed recently with good compression performance. However, since the specimen usually only tolerates low-power density illumination for long-term imaging with low phototoxicity, the image signal-to-noise ratio (SNR) is relatively low, which will cause the loss of some efficient position or intensity information using such lossy compression algorithms. Here, we propose a phase-space continuity-enhanced bzip2 (PC-bzip2) lossless compression method for LFM data as a high-efficiency and open-source tool that combines graphics processing unit-based fast entropy judgment and multicore-CPU-based high-speed lossless compression. Our proposed method achieves almost 10% compression ratio improvement while keeping the capability of high-speed compression, compared with the original bzip2. We evaluated our method on fluorescence beads data and fluorescence staining cells data with different SNRs. Moreover, by introducing temporal continuity, our method shows the superior compression ratio on time series data of zebrafish blood vessels.