In this paper, we present a novel licensed-shared access (LSA) spectrum-sharing scheme as an energy efficient way to increase the spectral utility of a network. We consider a two-tier network where a small cell network offers offloading services to a macro network to improve its quality of service. In return, the small cells are rewarded for their cooperation with a number of licenses to operate in the spectrum owned by the macro network. The short link distances and diversity offered by the small cell network to offload the macro user help enhance the total spectral and energy utilization of the network. For effective functioning of the scheme, it is important to determine the division between the fraction of small cells that provide offloading services and those which obtain the licenses. In this paper, we present a comprehensive mathematical model of this LSA-based offloading and evaluate the optimal division between the offloading and licensing small cells. Our analysis shows that such spectrum sharing can lead to commendable gains in the spectral utilization of the network while assuring the desired quality of service for both macro and small network. An intelligent determination of the fraction of offloading small cell network results in efficient energy use for offloading. We test our scheme within the network parameters of the city of Leeds, U.K. Our results indicate that the spectral utility of Leeds can be improved by more than 12×, and the energy efficiency by 16× through our proposed scheme.