Generic linkage preserves local complete intersection log canonical singularities

Let $S=\operatorname{Spec} R$ be a regular affine scheme over $k$, and let $X\subset S$ be a subscheme defined by $I=(z_1,\ldots,z_t)$ of codimension $r$. Let $M=(U_{ij})_{t\times r}$ be a matrix of variables, set $R'=R[U_{ij}]$, define $\alpha=(\alpha_1,\ldots,\alpha_r)=(z_1,\ldots,z_t)\cdot M$ and $J=[\alpha:IR']$, and set $Y=\operatorname{Spec} R'/J$. Generic-linkage conjecture. If $X$ is local complete intersection log canonical, then $Y$ is also local complete intersection log canonical. The question is motivated by the difficulty of transferring singularities from $X$ to its generic link, since there is no natural morphism from the link to $X$; the conjecture is presented as an open question.