We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue–Orlicz spaces of a discrete group $\Gamma$ and relative Toeplitz-Schur multipliers on Schatten–von-Neumann–Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum $\Lambda \,\subseteq \,\Gamma$, the norm of the Hilbert transformand the Riesz projection on Schatten–von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten–von-Neumann classes with exponent less than 1.