Electric dipole moments of atoms can arise from P-odd and T-odd electron--nucleon couplings. This work studies a general class of dimension-six electron--nucleon interactions mediated by Lorentz-violating tensors of ranks ranging from $1$ to $4$. The possible couplings are listed as well as their behavior under C, P, and T, allowing us to select the couplings compatible with electric-dipole-moment physics. The unsuppressed contributions of these couplings to the atoms hamiltonian can be read as equivalent to an electric dipole moment. The Lorentz-violating coefficients magnitudes are limited using electric-dipole-moment measurements at the levels of $3.2times10^{-31}text{(eV)}^{-2}$ or $1.6times10^{-33}text{(eV)}^{-2}$.
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