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Secure confirmation that a gravitational wave (GW) has been gravitationally lensed would bring together these two pillars of General Relativity for the first time. This breakthrough is challenging for many reasons, including: GW sky localization uncertainties dwarf the angular scale of gravitational lensing, the mass and structure of gravitational lenses is diverse, the mass function of stellar remnant compact objects is not yet well constrained, and GW detectors do not operate continuously. We introduce a new approach that is agnostic to the mass and structure of the lenses, compare the efficiency of different methods for lensed GW discovery, and explore detection of lensed kilonova counterparts as a direct method for localizing candidates. Our main conclusions are: (1) lensed neutron star mergers (NS–NS) are magnified into the ‘mass gap’ between NS and black holes, therefore selecting candidates from public GW alerts with high mass gap probability is efficient, (2) the rate of detectable lensed NS–NS will approach one per year in the mid-2020s, (3) the arrival time difference between lensed NS–NS images is $1\, \rm s\lesssim \Delta \mathit{ t}\lesssim 1\, yr$, and thus well-matched to the operations of GW detectors and optical telescopes, (4) lensed kilonova counterparts are faint at peak (e.g. rAB ≃ 24–26 in the mid-2020s), fade quickly ($d\lt 2\, \rm d$), and are detectable with target of opportunity observations with large wide-field telescopes. For example, just ≲ 0.25 per cent of Vera C. Rubin Observatory’s observing time will be sufficient to follow up one well-localized candidate per year. Our predictions also provide a physically well-defined basis for exploring electromagnetically the exciting new ‘mass gap’ discovery space.