A search for CP violation in Lambda(0)(b) -> pK(-) and Lambda(0)(b) -> p pi(-) decays is presented using the full Run 1 and Run 2 data samples of pp collisions collected with the LHCb detector, corresponding to an integrated luminosity of 9 fb(-1) at center-of-mass energies of 7, 8, and 13 TeV. For the Run 2 data sample, the CPviolating asymmetries are measured to be A(CP)(pK-) = (-1.4 +/- 0.7 +/- 0.4)% and A(CP)(p pi-)= (0.4 +/- 0.9 +/- 0.4)%, where the first uncertainty is statistical and the second is systematic. Following significant improvements in the evaluation of systematic uncertainties compared to the previous LHCb measurement, the Run 1 dataset is reanalyzed to update the corresponding results. When combining the Run 2 and updated Run 1 measurements, the final results are found to be A(CP)(pK-) = (-1.1 +/- 0.7 +/- 0.4)% and A(CP)(p pi-) = (0.2 +/- 0.8 +/- 0.4)%, constituting the most precise measurements of these asymmetries to date.