  The electron Lamb shift $(2P-2S)$ and the energy interval $(2S-1S)$ in
muon-electron ions of lithium, beryllium, and boron have been calculated within
the framework of the perturbation theory method for the fine structure constant
and the electron-muon mass ratio. The corrections of the first and second
orders of the perturbation theory, which include the effects of vacuum
polarization, nuclear structure and recoil, are taken into account. The
obtained analytical results in perturbation theory are compared with the
results of calculations within the variational approach. The obtained values
for the Lamb shift $(2P-2S)$ and the interval $(2S-1S)$ can be used for
comparison with future experimental data and verification of quantum
electrodynamics.
