In Prognostics and Health Management (PHM) sufficient prior observed degradation data is usually critical for Remaining Useful Lifetime (RUL) prediction. Most previous data-driven methods assume that training (source) and testing (target) condition monitoring data have similar distributions. However, due to different operating conditions, fault modes and noise, distribution and feature shift exist across different domains. This shift reduces the performance of predictive models when no target observed run-to-failure data is available. To address this issue, this paper proposes a new data-driven approach for domain adaptation in prognostics using Long Short-Term Neural Networks (LSTM). We use a Domain Adversarial Neural Network (DANN) approach to adapt remaining useful life estimates to a target domain containing only sensor information. We analyse our approach using the NASA Commercial Modular Aero-Propulsion System Simulation (C-MAPPS). The results show that the proposed method can provide more reliable RUL predictions than models trained only on source data for varying operating conditions and fault modes.