This paper investigates the use of a data-driven method to model the dynamics of the chaotic Lorenz system. An architecture based on a recurrent neural network with long and short term dependencies predicts multiple time steps ahead the position and velocity of a particle using a sequence of past states as input. To account for modeling errors and make a continuous forecast, a dense artificial neural network assimilates online data to detect and update wrong predictions such as non-relevant switchings between lobes. The data-driven strategy leads to good prediction scores and does not require statistics of errors to be known, thus providing significant benefits compared to a simple Kalman filter update.