Coal combustion residues and other geological waste materials have been proposed as a resource for rare earth elements (REEs, herein defined as the 14 stable lanthanides, yttrium, and scandium). The extraction of REEs from residues often generate acidified leachates that require highly selective separation methods to recover the REEs from other major soluble ions in the leachates. Here, we studied two liquid membrane processes (liquid emulsion membranes, LEM, and supported liquid membranes, SLM) and compared them to standard solvent extraction techniques for selective recovery and concentration of REEs from a leachate of coal fly ash. All separation methods involved an organic solution of di(2-ethylhexyl)phosphoric acid dissolved in kerosene or mineral oil and an acid strippant solution of 5 M nitric acid for the liquid-based separations. The LEM configuration, which separated REEs by immersing an acid-in-oil emulsion in the ash leachate, resulted in similar recovery percentages of individual REEs as the conventional solvent extraction approach. The recovery of REEs in the SLM configuration, which involved the impregnation of the solvent in a hydrophobic membrane, was slower than the LEM process. However, the SLM process was notably more selective for the heavy (and higher value) REEs, while the conventional extraction and LEM processes were more selective for the light REEs. A flux-based model of the extraction processes suggested that recovery rates were limited by REE affinity for the solvent chelator in the SLM, while the rates of REEs separation via LEM were limited by diffusive mass transfer across the liquid membrane. Altogether, these results help to identify specific steps in the recovery process that future work should target in the development of scalable liquid membrane separations for REE recovery.