In these proceedings, we summarize results from the first lattice-QCD calculation of the twist-3 axial quark GPDs for the proton using the large-momentum effective theory approach. The calculation is performed using one $N_f=2+1+1$ ensemble of maximally twisted mass fermions with a clover term, that has a volume $32^3\times64$, lattice spacing 0.0934 fm, and a pion mass of 260 MeV. The momentum boost of the nucleon matrix elements is 0.83, 1.25, and 1.67 GeV, and the 4-vector momentum transfer squared is 0.69, 1.38, and 2.76 GeV$^2$. We perform a number of consistency checks, such as the Burkhardt-Cottingham-type as well as Efremov-Teryaev-Leader-type sum rules.