Existing techniques for the simultaneous encryption and compression of three-dimensional (3D) image sequences (e.g., video sequences, medical image sequences) may come with sufficient decryption accuracy or compression ratio, but do not inherently have both; the relationship between them is generally ignored because the images of a sequence are handled individually. To address this problem, we designed Tensor Compressive Sensing (TCS) to simultaneously encrypt and compress a 3D sequence as a tensor rather than several 2D images. To further enhance security, a non-autonomous Lorenz system is constructed to control the three measurement matrices of TCS. The proposed method preserves the intrinsic structure of tensor-based 3D image sequences and achieves a favorable balance of compression ratio, decryption accuracy, and security. Numerical simulation results verify the validity and the reliability of the TCS scheme.