Surrogate modelling can alleviate the computational burden of design activities as they rely on multiple evaluations of high-fidelity models. However, the learning task can be adversely affected by the high-dimensionality of the system, complex non-linearities and temporal dependencies, leading to an inaccurate surrogate model. In this paper we present an innovative dual-phase Long-Short Term Memory (LSTM) Autoencoder-based surrogate model applied in an industrial context for the prediction of aircraft dynamic landing response over time, conditioned by an exogenous set of design parameters. The LSTM-Autoencoder is adopted as a dimensionality-reduction tool that extracts the temporal features and the nonlinearities of the high-dimensional dynamical system response, and learns a low-dimensional representation of it. Then, a Fully Connected Neural Network is trained to learn the simplified relationship between the input parameters and the reduced representation of the output. For our application, the results demonstrate that our LSTM-AE based model outperforms both Principal Component Analysis and Convolutional-Autoencoder based surrogate models, in predicting the parameters-dependent high-dimensional temporal system response.