We report the aqueous lyotropic mesophase behaviors of protonated amine-based "lipidoids," a class of synthetic lipid-like molecules that mirrors essential structural features of the multitail bacterial amphiphile lipid A. Small-angle X-ray scattering (SAXS) studies demonstrate that the protonation of the tetra(amine) headgroups of six-tail lipidoids in aqueous HCl, HNO3, H2SO4, and H3PO4 solutions variably drives their self-assembly into lamellar (L-alpha) and inverse micellar (I-II) lyotropic liquid crystals (LLCs), depending on acid identity and concentration, amphiphile tail length, and temperature. Lipidoid assemblies formed in H2SO4(aq) exhibit rare inverse body-centered cubic (BCC) and inverse face-centered cubic (FCC) micellar morphologies, the latter of which unexpectedly coexists with zero mean curvature L-alpha phases. Complementary atomistic molecular dynamics (MD) simulations furnish detailed insights into this unusual self-assembly behavior. The unique aqueous lyotropic mesophase behaviors of ammonium lipidoids originate in their dichotomous ability to adopt both inverse conical and chain-extended molecular conformations depending on the number of counterions and their identity, which lead to coexisting supramolecular assemblies with remarkably different mean interfacial curvatures.