Light hole doping of lanthanum cuprate strongly suppresses the onset of antiferromagnetic (AF) order. Surprisingly, it simultaneously suppresses the extrapolated zero temperature sub-lattice magnetization. 139La NQR results in lightly Li-doped lanthanum cuprate have demonstrated that these effects are independent of the details of the mobility of the added holes. We propose a model in which doped holes phase separate into charged domain walls that surround ``anti-phase domains. These domains are mobile down to ~30 K where they either become pinned to the lattice or evaporate as their constituent holes become pinned to dopant impurities.