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Fast radio bursts (FRBs) are cosmological subsecond bursts of coherent radio emission, whose source is still unknown. To date, the Galactic magnetar SGR 1935 + 2154 is the only astrophysical object known to emit radio bursts akin to FRBs, albeit less powerful, supporting suggestions that FRBs originate from magnetars. Many remarkable properties of FRBs-e.g., the dichotomy between repeaters and one-off sources, and their power-law energy distributions (with typical index similar to 2-3)-are not well understood yet. Moreover, the huge radio power released by the most active repeaters is challenging even for the magnetic energy reservoir of magnetars. Here, we assume that FRBs originate from corotating hotspots anchored in neutron star (NS) magnetospheres and occasionally get amplified by large factors via gravitational self-lensing in the strong NS field. We evaluate the probability of amplification and show that: (i) a power-law energy distribution of events proportional to E -(2-3) is generally expected; (ii) all FRB sources may be regarded as repeating, their appearance as one-off sources or repeaters being determined by the critical dependence of the amplification probability on the emission geometry and source orientation relative to Earth; and (iii) the most active repeaters, in particular, correspond to extremely rare and finely tuned orientations (similar to 1 in 106), leading to large probabilities of amplification that make their bursts frequently detectable. At the same time, their power release appears enhanced, typically by factors greater than or similar to 10, easing their energy budget problem.