Polycrystalline samples of La4LiMnO8 and La3SrLiMnO8 have been studied by a combination of X-ray diffraction (XRD), neutron diffraction (ND), Li-6 MAS NMR, electron microscopy (EM), and magnetometry. Room-temperature XRD and ND measurements suggest that both compounds have the K2NiF4 structure, with a disordered arrangement of Li and Mn over the six-coordinate sites. However, MAS NMR and EM demonstrate the presence of local 1:1 Li:Mn order on these sites, and EM shows that although cation order is well-developed in each xy sheet of corner-sharing octahedra, the sheets are stacked randomly along z. The structures are best described as paracrystalline, and many of the concepts of conventional crystallography are inapplicable. Magnetometry and low-temperature ND experiments show that, despite their paracrystallinity, the two compounds are ordered antiferromagnetically with susceptibility maxima at 26 and 18 K, respectively, and with ordered magnetic moments of 3.61(6) and 2.3(1) mu(B) per Mn cation at 2 K. Anisotropic peak broadening reveals a 2D character in the magnetic behavior of both compounds, and La3SrLiMnO8 is well-modeled as a quadratic layer S = 3/2 Heisenberg antiferromagnet.