The Lorenz-63 model mimics some features of the atmosphere and the climate system, like their chaotic behavior and the existence of preferred regimes. Furthermore, distinct regions on the Lorenz attractor show different predictabilities, exactly as distinct types of weather situations are endowed with different predictability horizons. Finally, changes in the frequency of occurrence of regimes can be observed in the real system and in the toy Lorenz model, when external forcings increase. In this framework, the ability of a neural network (NN) model to recognize regions of distinct predictability on the Lorenz attractor is shown, even vs. dynamical estimations. Moreover, once added an external forcing to the Lorenz system (as a toy simulation of increase in anthropogenic forcings to the climate system), changes of predictability in this new scenario are found by both dynamical quantities and NN modeling. Attempts at an “operational” NN estimation of predictability are investigated, too.