Reaction of LaSrMnO4 with CaH2 at 420 degrees C yields LaSrMnO3.67(3). Raising the temperature to 480 degrees C yields the Mn(II) phase LaSrMnO3.50(2).Neutron powder diffraction data show both phases adopt body-centred orthorhombic crystal structures (LaSrMnO3.67(3), Immm: a = 3.7256(1) angstrom, b = 3.8227(1) angstrom, c = 13.3617(4) angstrom; LaSrMnO3.50(2), Immm: a = 3.7810(1) angstrom, b = 3.7936(1) angstrom, c = 13.3974(3) angstrom) with anion vacancies located within the equatorial MnO2-x planes of the materials. Analogous reactivity is observed between LaBaMnO4 and CaH2 to yield body-centred tetragonal reduced phases (LaBaMnO3.53(3), I4/mmm: a = 3.8872(1) angstrom, c = 13.6438(2) angstrom). Low-temperature neutron diffraction and magnetisation data show that LaSrMnO3.5 and LaBaMnO3.5 exhibit three-dimensional antiferromagnetic order below 155 K and 135 K respectively. Above these temperatures, they exhibit two-dimensional antiferromagnetic order with paramagnetic behaviour observed above 480 K in both phases. The origin of the low dimensional magnetic order and ordering of the anion vacancies in the reduced phases is discussed.