We investigate the potential of the Large Hadron Collider (LHC) to probe one of the most compelling beyond the Standard Model frameworks - walking technicolor (WTC), involving strong dynamics and having a slowly running (walking) new strong coupling. For this purpose we use recent LHC Run 2 data to explore the full parameter space of the minimal WTC model using dilepton signatures from heavy neutral Z′ and Z′′ resonances predicted by the model. This signature is the most promising one for discovery of WTC at the LHC for the low-intermediate values of the g coupling - one of the principle parameters of WTC. We have demonstrated complementarity of the dilepton signals from both resonances, established the most up-to-date limit on the WTC parameter space, and provided projections for the LHC potential to probe the WTC parameter space at higher future luminosities and upgraded energy. We have explored the whole four-dimensional parameter space of the model and have found the most conservative limit on the WTC scale MA above 3 TeV for the low values of g, which is significantly higher than previous limits established by the LHC collaborations.