In this study, we have calculated the average energies of the ground and excited configurations of a lithium atom enclosed by a spherical potential well with finite barrier height, and we have also carried out calculations of orbital energies, confining potential energies and probabilities of finding the electrons in 1s and nl orbitals as a function of confinement radius for the 1s2nl configurations [nl = 2s, 2p, 3d and 4f]. Quantum Genetic Algorithm (QGA) and Hartree-Fock Roothaan (HFR) methods are used to calculate the energy eigenvalues and corresponding wave functions of the confined system. The results show that potential barrier height and confinement radius have a strong influence on the energies and the probabilities of finding the electrons inside and outside the well. It is found that 1s orbital energy increases suddenly at a critical confinement radius, at which the electron in nl orbital is trapped by the confining potential.