Motivated by the success of deep learning in recent years, prediction-based methods are used to compress satellite telemetry data. In this paper, two-stage lossless compression methods for telemetry data are demonstrated. In the first stage, different approaches of long short-term memory (LSTM) based on one-to-one, many-to-one, and many-to-many network architectures are presented. The framework of implementing each approach, as a predictor, is discussed. In the second stage, a set of competing entropy coding methods are tested and evaluated. The presented approaches are capable of exploring correlation dependencies between consecutive samples in the individual and/or successive telemetry frames. The proposed approaches are introduced in two different versions: stacked- and nonstacked-based LSTM architectures trying to achieve higher prediction efficiency. The proposed approaches are tested on real telemetry data, in frames of different data word widths, in distinct FUNcube satellite sessions. The performance of each presented approach, as a predictor, is evaluated based on prediction gain, and reduction in entropy. However, the performance of the whole two-stage lossless compression method is assessed by compression ratio. Comparative analysis is preformed among the proposed approaches, and the improvements are verified against the state-of-the-art prediction-based approaches.