Let ${\mathcal{I}}_{\alpha ,m}$ be the multilinear $\theta$-type generalized fractional integrals and ${\overrightarrow{b}}_{\sigma }$ be the vector with each $b_{{\sigma }_i}\in \widetilde{\mathrm{R}\mathrm{B}\mathrm{M}\mathrm{O}}\left(\mu \right)$. The boundedness for ${\mathcal{I}}_{\alpha ,m}$ and the iterated multi-commutators ${\mathcal{I}}_{\alpha ,m,{\overrightarrow{b}}_{\sigma }}$ on Lebesgue spaces over non-homogeneous spaces are showed in this paper.