We evaluate recently developed randomized matrix decomposition methods for fast lossless compression and reconstruction of hyperspectral imaging (HSI) data. The simple random projection methods have been shown to be effective for lossy compression without severely affecting the performance of object identification and classification. We build upon these methods to develop a new double-random projection method that may enable security in data transmission of compressed data. For HSI data, the distribution of elements in the resulting residual matrix, i.e., the original data subtracted by its low-rank representation, exhibits a low entropy relative to the original data that favors high-compression ratio. We show both theoretically and empirically that randomized methods combined with residual-coding algorithms can lead to effective lossless compression of HSI data. We conduct numerical tests on real large-scale HSI data that shows promise in this case. In addition, we show that randomized techniques can be applicable for encoding on resource-constrained on-board sensor systems, where the core matrix-vector multiplications can be easily implemented on computing platforms such as graphic processing units or field-programmable gate arrays.