Fink et al. (2020) showed that the Schubert polynomial \(\mathfrak{S}_w(x)\) is zero-one if and only if w avoids twelve permutation patterns. In this paper, we prove that the Grothendieck polynomial \(\mathfrak{G}_w(x)\) is zero-one, i.e., with coefficients either 0 or ±1, if and only if w avoids six patterns. As applications, we show that the normalized double Schubert polynomial \(N(\mathfrak{S}_w(x;y))\) is Lorentzian when \(\mathfrak{G}_w(x)\) is zero-one, partially confirming a conjecture of Huh et al. (2022). Moreover, we verify several conjectures on the support and coefficients of Grothendieck polynomials posed by Mészáros et al. (2025) for the case of zero-one Grothendieck polynomials.
