Large-scale relativistic configuration-interaction calculation of energy levels of core-excited states of lithiumlike ions is presented. Quantum electrodynamic, nuclear recoil, and frequency-dependent Breit corrections are included in the calculation. The approach is consistently applied for calculating all n = 2 core-excited states for all lithium-like ions starting from argon (Z = 18) and ending with krypton (Z = 36). The results obtained are supplemented with systematical estimations of calculation errors and omitted effects.