Lithium storage and capture are of particular importance for the development of new technology in electric vehicles and portable electronics. Nanotubes (NTs) are among many porous nanomaterials offered as potential candidates for lithium storage. In this paper, we adopt a continuum approach together with the Lennard–Jones function to determine the minimum interaction energies for lithium atoms in boron nitride nanotubes (BNNTs) and carbon nanotubes (CNTs). By minimizing the interaction energies, we may obtain the preferred type and size of the nanotubes to encapsulate the lithium atoms. The results showed that BNNTs and CNTs are attractive candidates for lithium atom encapsulation, and the optimal nanotube to enclose lithium is the BNNT with a radius equal to 3.4 Å, and corresponding (5, 5) armchair nanotubes and (9, 0) zigzag nanotubes, where the minimum energy is obtained. The present computations observed that both nanotubes are promising candidates for lithium intercalation materials suitable for battery applications.