We have studied concentrated equimolar mixtures of tetradecanoic acid (myristic acid, C13COOH) and hexadecyltrimethylammonium hydroxide (CTAOH) in which the OH- counterions are gradually exchanged by other anions (Cl-, Br-, CH3COO-, CH3-(C6H4)-SO3-). We demonstrate that the stability of a Lbeta phase can be achieved at equimolarity between both surfactants, provided that the phase contains also a sufficient number of anions exchanged with OH-. In the absence of exchange (equimolar mixture of C13COOH and CTAOH), a three-dimensional crystalline Lc phase is produced. As the OH- ions are replaced by other ions, a swollen Lbeta lamellar phase appears, first in coexistence with the Lc (D* = 400 A) and then in coexistence with a dilute phase only (D* = 215 A). In the latter regime, the repeating distance depends very little on the exchange ratio, but rather on the nature of the counterion. If too many OH- ions are exchanged, the Lbeta phase becomes unstable again. A Poisson-Boltzmann model with charge regulation computed for a closed system predicts qualitatively the existence of this narrow domain of stability for the Lbeta phase.