Grinding together the solid acid HLaTiO4 with stoichiometric quantities of lithium hydroxide monohydrate gives the solid solution H1-xLixLaTiO4. The structures of these crystalline phases have been refined against neutron powder diffraction data to show that all of these compounds crystallize in the centrosymmetric space group P4/nmm. The protons and lithium cations occupy sites between the perovskite layers; the former in hydroxide groups that hydrogen-bond to adjacent layers while Li+ is in four-coordinate sites that bridge the perovskite slabs with a geometry intermediate between square-planar and tetrahedral. The reaction proceeds rapidly, but the unit cell size continues to evolve over the course of days with a gradual compression along the interlayer direction that can be modeled using a power law dependence reminiscent of an Ostwald ripening process. On heating, these materials undergo a mass loss because of dehydration but retain the layered Ruddlesden-Popper structure up to 480 degrees C before a substantial loss of crystallinity on further heating to 600 degrees C. Impedance spectroscopy studies of the dehydrated materials shows that Li+ mobility in these materials is lower than the LiLaTiO4 end member, possibly because of microstructural effects causing large intergrain resistance through the defective phases.