Root-of-unity limit of the $A_{n-1}$ lens elliptic gamma function solution of the star-star relation

We study the root-of-unity limit of the multi-component spin solution of the star-star relation whose Boltzmann weights are products of lens elliptic gamma functions, and whose spins take values in $\mathbb{R}^{n-1}\times(\mathbb{Z}_r)^{n-1}$. When one of the elliptic nomes tends to a primitive $2rN