The 2s(1/2)-2p(1/2) energy splittings DeltaE(L) of the lithiumlike ions 19779Au76+, 20882Pb79+, and 23892U89+ have been measured at the Experimental Storage Ring, utilizing low energy dielectronic recombination. The resonance energies in total 41 different 1s(2) 2p(1/2)nl(j(')) (n > or =20) autoionizing Rydberg states populated in the dielectronic capture process have been determined. The 2s(1/2)-->2p(1/2) excitation energies have been obtained by extrapolation of these resonance energies to the associated series limits n--> infinity. The combined analysis of the experimental data for all three ions yields DeltaE(L)=216.134(96) eV for Au76+, 230.650(81) eV for Pb79+, and 280.516(99) eV for U89+.