We have probed the influence of salt and temperature on the spatial periodicity (d) of the fluid lamellar (Lα) phase formed by two ionic amphiphiles, whose bilayer bending rigidity moduli are widely different. In the case of rigid 1,2-dimyristoyl-3-trimethylammonium-propane (chloride salt) (DMTAP) bilayers, d is found to decrease with increasing salt concentration (Cs) in the solution, in qualitative agreement with the DLVO theory. d depends only very weakly on temperature in this system. On the other hand, in the Lα phase formed by highly flexible didodecyldimethylammonium chloride (DDAC) bilayers, d is not set by the minimum of the DLVO potential over a wide range of Cs, due to inter-bilayer repulsion arising from thermal undulations of the bilayers. An abrupt transformation of this undulation stabilized swollen Lα phase into a collapsed Lα phase, where d is comparable to the bilayer thickness, is observed above a threshold value of Cs. At higher Cs an unbinding transition of the bilayers is observed on heating, where the collapsed Lα phase transforms into a dispersion of spatially uncorrelated bilayers. Our observations are consistent with this transition being first-order.