We investigate the structure of the neutron-rich $\ensuremath{\Lambda}$-hypernucleus ${}_{\ensuremath{\Lambda}}^{10}\mathrm{Li}$ by using microscopic shell-model calculations considering a $\ensuremath{\Lambda}$-$\ensuremath{\Sigma}$ coupling effect. The calculated $\ensuremath{\Sigma}$-mixing probability in the ${}_{\ensuremath{\Lambda}}^{10}\mathrm{Li}$ ground state is found to be about 0.34% that is coherently enhanced by the $\ensuremath{\Lambda}$-$\ensuremath{\Sigma}$ coupling configurations, leading to the energy shift 0.28 MeVthat is about 3 times larger than that in ${}_{\ensuremath{\Lambda}}^{7}\mathrm{Li}$. The importance of the $\ensuremath{\Sigma}$ configuration obtained by the $\ensuremath{\Sigma}N$ interaction and the potentiality of the neutron-rich environment are discussed.