Data assimilation is a fundamental process for estimating optimal initial conditions in numerical prediction systems through the combination of prior model forecasts (background states) and observational data. The resulting estimate is referred to as the analysis. In this study, a Cellular Neural Network (Cell-NN) is investigated as a data assimilation (DA) approach. In addition, the Cell-NN framework is employed for the time integration of dynamical systems. Distinct Cell-NN configurations are developed for both the data assimilation procedure and the integration scheme. The Lorenz system, operating in a chaotic dynamical regime, is used as a benchmark to evaluate the proposed methodology. For comparison, data assimilation using the three-dimensional variational (3D-Var) method is also implemented. The Cell-NN belongs to the class of unsupervised neural networks. The results demonstrate that the analysis produced by the Cell-NN exhibits error magnitudes comparable to those obtained with the 3D-Var technique.