  This paper proposes to exploit gravitational lensing effects to improve the
sensitivity of neutrino telescopes to the intrinsic neutrino emission of
distant blazar populations. This strategy is illustrated with a search for
cosmic neutrinos in the direction of four distant and gravitationally lensed
Flat-Spectrum Radio Quasars. The magnification factor is estimated for each
system assuming a singular isothermal profile for the lens. Based on data
collected from 2007 to 2012 by the ANTARES neutrino telescope, the strongest
constraint is obtained from the lensed quasar B0218+357, providing a limit on
the total neutrino luminosity of this source of $1.08\times
10^{46}\,\mathrm{erg}\,\mathrm{s}^{-1}$. This limit is about one order of
magnitude lower than those previously obtained in the ANTARES standard point
source searches with non-lensed Flat-Spectrum Radio Quasars.
