In order to clarify the polymorphism in the lithium sulfate family, LiREx(NH4)1 - xSO4 (0.5 [less-than or equal to] x [less-than or equal to] 4.0 mol%, nominal value; RE = Er3+, Yb3+ and Dy3+) crystals were grown from aqueous solution by slow evaporation between 298 and 313 K. The doping of the samples allowed us to obtain two polymorphic forms, [alpha] and [beta], of LiNH4SO4 (LAS). By means of X-ray diffraction (XRD) in single crystals, we determined the crystal structures of two new [alpha]-polytypes, which we have named [alpha]1- and [alpha]2-LAS. They present the same space group P21/c and the following relation among their lattice parameters: a2 = -c1, b2 = -b1, c2 = -2a1 - c1. In order to evaluate the stability of the new [alpha]-polytypes, we performed thermal analysis, X-ray diffraction and dielectric spectroscopy on single crystals and polycrystalline samples over the cyclic temperature range: 190 [rightwards arrow] 575 [rightwards arrow] 190 K. The results obtained by all the techniques used in this study demonstrate that [alpha]-polytypes are stable across a wide range of temperatures and they show an irreversible phase transition to the paraelectric [beta]-phase above 500 K. In addition, a comparative study of [alpha]- and [beta]-polytypes shows that both polymorphic structures have a common axis, with a possible intergrowth that facilitates their coexistence and promotes the reconstructive [alpha] [rightwards arrow] [beta] transition. This intergrowth was related to small anomalies detected between 240 and 260 K, in crystals with an [alpha]-habit.