The stability of lithium atoms in alpha-rhombohedral boron was investigated by first-principles calculations of total energies and molecular dynamics (MD) simulations. In the case of a low concentration (1.03 at. %), Li at the center of the icosahedral B-12 site (the I-site) had a negative binding energy, which suggests Li at the I-site is unstable. However, MD simulations at temperatures below 750 K indicated that Li is still confined in the B12 cage under these conditions, which means Li at the I-site is metastable. Over 800 K, Li began to move away from the B-12 site and settled at the tetrahedral site (the T-site) or at the octahedral site (the O-site). Li at the T-site also had a negative binding energy, but MD simulations indicated it was metastable up to 1400 K and did not move to other sites. Li at the O-site was energetically the most favorable, having a positive binding energy. In the case of a high concentration (7.69 at. %), the I-site changed to an unstable saddle point. At this concentration, the T-site was metastable and the O-site became the most stable. In MD simulations at 1400 K, Li atoms at the O-site never jumped to other sites regardless of concentration. Considering these facts, the diffusion coefficient of Li in a-rhombohedral boron would have to be very small below 1400 K.