A systematic QED treatment of the electron correlation is presented for ions along the lithium isoelectronic sequence. We start with the zeroth-order approximation that accounts for a part of the electron-electron interaction by a local model potential introduced into the Dirac equation. The residual electron correlation is treated by perturbation theory. A rigorous QED evaluation is presented for the first two terms of the perturbative expansion; the third-order contribution is calculated within the many-body perturbation theory. We report accurate numerical results for the electronic-structure part of the ionization potential for the n=2 states of all Li-like ions up to uranium.