Energy levels and fine-structure intervals of the 1s2l2l′ core-excited states are calculated for ions along the Li isoelectronic sequence from argon to uranium. The calculation is performed by the relativistic configuration-interaction method adapted for treatment of autoionizing core-excited states. The calculational approach includes the relativistic treatment of the nuclear recoil effect, the leading quantum electrodynamics (QED) shifts as delivered by the model QED operator, and the frequency dependence of the Breit interaction. The 1s2l2l′–1s22l transition energies are obtained by combining the present results for the 1s2l2l′ states with energies of the 1s22l states compiled from previous calculations. All theoretical energies are supplied with uncertainty estimates. Our theoretical predictions for the 1s2l2l′–1s22l transitions are significantly more accurate than the best experimental results available today and can be used for calibrating experimental X-ray spectra.