We present observations of two strong-lensing galaxy clusters located within the 90 per cent credible sky localization maps released following LIGO–Virgo’s discovery of the binary black hole (BH–BH) gravitational wave (GW) source GW170814. Our objectives were (1) to search for candidate electromagnetic (EM) counterparts to GW170814 under the hypothesis that it was strongly lensed, and thus more distant and less massive than inferred by LIGO–Virgo, and (2) to demonstrate the feasibility of rapid target of opportunity observations to search for faint lensed transient point sources in crowded cluster cores located within GW sky localizations. Commencing 20 h after discovery, and continuing over 12 nights, we observed Abell 3084 (z = 0.22) and SMACS J0304.3 − 4401 (z = 0.46) with GMOS on the Gemini-South telescope, and Abell 3084 with MUSE on ESO’s Very Large Telescope. We detect no candidate EM counterparts in these data. Calibration of our photometric analysis methods using simulations yields 5σ detection limits for transients in difference images of the cores of these clusters of i = 25. This is the most sensitive photometric search to date for counterparts to GW sources, and rules out the possibility that GW170814 was lensed by these clusters with a kilonova-like EM counterpart. Based on the detector frame masses of the compact objects, and assuming that at least one neutron star (NS) is required in the merging system to produce a kilonova-like counterpart, implies that GW170814 was neither an NS–NS nor NS–BH merger at z > 8 lensed by either of these clusters. Also, in the first ever emission line search for counterparts to GW sources, we detected no lines down to a 5σ detection limit of |$5\times 10^{-17}\, {\rm erg\, s^{-1}\, cm^{-2}}$|⁠.