By using the newly developed Python library JAX, we developed a fast and differentiable large-eddy simulation model, named LEX. Evaluated with a warm bubble case, LEX maintains high accuracy as the Cloud Model 1. With the hardware acceleration and better numerical stability, LEX can be quite faster. To report its differentiability, we further trained a deep learning-based parameterization scheme. The newly trained model can surpass the conventional scheme and get proper forecast results.