We consider the evolution of the phase transition from the parent hexagonal phase ${P6}_{3}/mmc$ to the orthorhombic phase $\mathrm{Pmcn}$ that occurs in several compounds of the ${A}_{2}{\mathrm{BX}}_{4}$ family and depends on the hcp lattice parameter $c/a.$ For compounds of ${\mathrm{K}}_{2}{\mathrm{SO}}_{4}$ type with $c/a$ larger than the threshold value 1.26 the direct first-order transition $\mathrm{Pmcn}\ensuremath{\leftrightarrow}{P6}_{3}/mmc$ is characterized by a large entropy jump $\ensuremath{\sim}R\mathrm{ln}2.$ For compounds ${\mathrm{Rb}}_{2}{\mathrm{WO}}_{4},{\mathrm{K}}_{2}{\mathrm{MoO}}_{4},{\mathrm{K}}_{2}{\mathrm{WO}}_{4}$ with $c/a<1.26$ this transition occurs via an intermediate incommensurate $(\mathrm{Inc})$ phase. Differential scanning calorimetry measurements were performed in ${\mathrm{Rb}}_{2}{\mathrm{WO}}_{4}$ to characterize the thermodynamics of the $\mathrm{Pmcn}\ensuremath{\leftrightarrow}\mathrm{Inc}\ensuremath{\leftrightarrow}{P6}_{3}/mmc$ transitions. It was found that both transitions are again of the first order with entropy jumps $0.2\ensuremath{\cdot}R\mathrm{ln}2$ and $0.3\ensuremath{\cdot}R\mathrm{ln}2.$ Therefore at $c/a\ensuremath{\sim}1.26$ the ${A}_{2}{\mathrm{BX}}_{4}$ compounds reveal an unusual Lifshitz point where three first-order transition lines meet. We propose the coupling of crystal elasticity with ${\mathrm{BX}}_{4}$ tetrahedra orientation as a possible source of the transitions discontinuity.