  The random dipolar magnet LiHo$_x$Y$_{1-x}$F$_4$ enters a strongly frustrated
regime for small Ho$^{3+}$ concentrations with $x<0.05$. In this regime, the
magnetic moments of the Ho$^{3+}$ ions experience small quantum corrections to
the common Ising approximation of LiHo$_x$Y$_{1-x}$F$_4$, which lead to a
$Z_2$-symmetry breaking and small, degeneracy breaking energy shifts between
different eigenstates. Here we show that destructive interference between two
almost degenerate excitation pathways burns spectral holes in the magnetic
susceptibility of strongly driven magnetic moments in LiHo$_x$Y$_{1-x}$F$_4$.
Such spectral holes in the susceptibility, microscopically described in terms
of Fano resonances, can already occur in setups of only two or three frustrated
moments, for which the driven level scheme has the paradigmatic
$\Lambda$-shape. For larger clusters of magnetic moments, the corresponding
level schemes separate into almost isolated many-body $\Lambda$-schemes, in the
sense that either the transition matrix elements between them are negligibly
small or the energy difference of the transitions is strongly off-resonant to
the drive. This enables the observation of Fano resonances, caused by many-body
quantum corrections to the common Ising approximation also in the thermodynamic
limit. We discuss its dependence on the driving strength and frequency as well
as the crucial role that is played by lattice dissipation.
