Digital twins are increasingly developed to support the development, operation, and maintenance of cyber-physical systems such as industrial elevators. However, industrial elevators continuously evolve due to changes in physical installations, introducing new software features, updating existing ones, and making changes due to regulations (e.g., enforcing restricted elevator capacity due to COVID-19), etc. Thus, digital twin functionalities (often built on neural network-based models) need to evolve themselves constantly to be synchronized with the industrial elevators. Such an evolution is preferred to be automated, as manual evolution is time-consuming and error-prone. Moreover, collecting sufficient data to re-train neural network models of digital twins could be expensive or even infeasible. To this end, we propose unceRtaInty-aware tranSfer lEarning enriched Digital Twins LATTICE, a \textit{transfer learning} based approach capable of transferring knowledge about the waiting time prediction capability of a digital twin of an industrial elevator across different scenarios. LATTICE also leverages \textit{uncertainty quantification} to further improve its effectiveness. To evaluate LATTICE, we conducted experiments with 10 versions of an elevator dispatching software from Orona, Spain, which are deployed in a Software in the Loop (SiL) environment. Experiment results show that LATTICE, on average, improves the Mean Squared Error by 13.131% and the utilization of uncertainty quantification further improves it by 2.71%.