We have measured the widths and energies of the 1s2s2p2P1/2,3/2→1s22s2S1/2 transitions in lithiumlike sulfur and argon, as well as the energies of the forbidden 1s2s2p4P5/2→1s22s2S1/2 M2 transition in both elements. All measurements were performed with a double-flat-crystal spectrometer without the use of any reference line. The transition energy measurements have accuracies ranging from 2.3 to 6.4 ppm depending on the element and line intensity. The widths and the intensity ratios of the 1s2s2p2P1/2,3/2→1s22s2S1/2 lines have also been measured. These are reference-free measurements of transitions in core-excited lithiumlike ions and have an accuracy comparable to the best relative measurements. We have also performed multiconfiguration Dirac-Fock calculations of the widths, energies, and intensity ratios. An extensive comparison between existing experimental results and theory is performed, and Bayesian techniques are employed to extract the energy of the 1s2p24P1/2→1s22p2P1/2 transition in sulfur and identify contaminant transitions.