Results are presented from a search for natural gauge-mediated supersymmetry (SUSY) in a scenario in which the top squark is the lightest squark, the next-to-lightest SUSY particle is a bino-like neutralino, and the lightest SUSY particle is the gravitino. The strong production of top squark pairs can produce events with pairs of top quarks and neutralinos, with each bino-like neutralino decaying to a photon and a gravitino. The search is performed using a sample of pp collision data accumulated by the CMS experiment at root s = 8 TeV, corresponding to an integrated luminosity of 19.7 fb(-1). The final state consists of a lepton (electron or muon), jets, and one or two photons. The imbalance in transverse momentum in the events is compared with the expected spectrum from standard model processes. No excess event yield is observed beyond the expected background, and the result is interpreted in the context of a general model of gauge-mediated SUSY breaking that leads to exclusion of top squark masses below 650-730 GeV.