This paper aims to calculate potential energy savings for space heating and hot water by 2030 for the Lithuanian building sector by implementing energy efficiency solutions. Policy recommendations are derived by showing which buildings and energy efficiency measures should be addressed in order to determine the full energy saving potential in the most effective way. Different cost curves for energy savings potential are applied, and these curves show the investor perspective and overall economic perspective. Final energy demand can be reduced by 56% by year 2030 if the least-cost energy efficiency solutions for each building type are selected. Energy performance class A implementation for the apartment buildings built before 1990 and supplied by district heating is the most cost-effective measure. If we consider the overall economic perspective, energy performance class A+ + (deep renovation) for the same buildings is the most cost-effective measure. The results call for (I) policies to support building renovation that address buildings with low energy performance instead of subsidising energy prices and (II) policies promoting deep renovation (A +, A+ +) in order to avoid lock-in effects and ensure the transition of the Lithuanian building stock towards nearly zero-energy buildings (nZEBs).