The objective of this research was to construct energy intensity forecasting models for key manufacturing industries, with a particular focus on “catching up” European economies. Future energy intensity values serve as the foundation for energy demand forecasts, which are essential inputs for the analysis of countries’ decarbonisation scenarios. The Lithuanian case is analysed in the context of its efforts to reach the economic development level of the most advanced European Union (EU) countries. The scientific literature and energy policy analysis, interdependence (correlation and regression), tendency and case analysis, logical economic reasoning, and graphical representation methods have been applied. The energy intensity forecasts until 2050 were based on historical statistical data of value added and final energy consumption of EU countries from 2000 to 2021. The analysis of historical trends revealed a remarkable decrease in industrial energy intensity in most EU countries, including Lithuania. Given the rapid pace of decline in historical energy intensity, the values observed in individual Lithuanian industries have already reached levels comparable to the most economically advanced EU countries. Four econometric trendlines were employed to construct forecasting models for energy intensity. The results for Lithuania demonstrated that the selected trendlines exhibited a high degree of fit with historical energy intensity data from the EU, as evidenced by their R2 values. Furthermore, the forecasts were shown to be highly accurate, with their MAPEs remaining below 10% in most cases. Nevertheless, the logarithmic trendline was found to be the most accurate for forecasting energy intensity in total manufacturing (MAPE = 4.0%), non-metallic minerals (MAPE = 3.5%), and food, beverages, and tobacco (MAPE = 4.1%) industries, with the exponential trendline in the chemical industry (MAPE = 8.7%) and the moving average in the total manufacturing industry (MAPE = 4.0%), food industries (MAPE = 4.0%), and remaining aggregate industries (MAPE = 14.5%). It is forecasted that energy intensity could decline by 8 to 16% to 1.10–1.20 kWh/EUR in Lithuania’s manufacturing industries by 2050.