We consider a joint survival and mixed-effects model to explain the survival time from longitudinal data and high-dimensional covariates. The longitudinal data is modeled using a nonlinear mixed-effects model, where the regression function serves as a link function incorporated into a Cox model. In that way, the longitudinal data is related to the survival time. Additionally, the Cox model takes into account the inclusion of high-dimensional covariates. The main objectives of this research are two-fold: first, to identify the relevant covariates that contribute to explaining survival time, and second, to estimate all unknown parameters of the joint model. For that purpose, we consider the estimate defined through maximizing a Lasso penalized likelihood. To tackle the optimization problem, we implement a preconditioned stochastic gradient to handle the latent variables of the nonlinear mixed-effects model associated with a proximal operator to manage the non-differentiability of the penalty. We provide relevant simulations that showcase the performance of the proposed variable selection and the parameter estimation method in the joint modeling of the Cox and logistic model.