Comment on `Oxygen vacancy-induced magnetic moment in edge-sharing CuO$_{2}$ chains of Li$_{2}$CuO$_{2}$'

In a recent work devoted to the magnetism of Li$_{2}$CuO$_{2}$, Shu et al. [New J. Phys. 19 (2017) 023026] have proposed a "simplified" unfrustrated microscopic model that differs considerably from the models refined through decades of prior work. We show that the proposed model is at odds with known experimental data, including the reported magnetic susceptibility $\chi(T)$ data up to 550~K. Using an 8$^{\rm th}$ order high-temperature expansion for $\chi(T)$, we show that the experimental data for Li$_{2}$CuO$_{2}$ are consistent with the prior model derived from inelastic neutron scattering (INS) studies. We also establish the $T$-range of validity for a Curie-Weiss law for the real frustrated magnetic system. We argue that the knowledge of the long-range ordered magnetic structure for $T<T_N$ and of $\chi(T)$ in a restricted $T$-range provides insufficient information to extract all of the relevant couplings in frustrated magnets; the saturation field and INS data must also be used to determine several exchange couplings, including the weak but decisive frustrating antiferromagnetic (AFM) interchain couplings.