Ionic-liquid-based acidic aqueous biphasic solutions (AcABSs) recently offered a breakthrough in the field of metal recycling. The particular mixture of tributyltetradecylphosphonium chloride ([P4,4,4,14]Cl), acid, and water presents the unusual characteristic of a lower solution critical temperature (LCST), leading to phase separation upon a temperature rise of typically a few tens of degrees. We address here the microscopic mechanisms driving the phase separation. Using small-angle neutron scattering, we characterized the spherical micelle formation in a binary ionic liquid/water solution and the micelle aggregation upon the addition of acid due to the screening of electrostatic repulsion. The increase in both the acid concentration and the temperature eventually leads to micelle flocculation and phase separation. This last step is achieved through chloride ion adsorption at the surface of the micelle. This exothermic adsorption compensates for the entropic cost, leading to a counterintuitive behavior, and may be generalized to a number of molecular systems with an LCST.