  We reformulate the Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$
of Lie algebras of type D via the theory of canonical bases arising from
quantum symmetric pairs initiated by Weiqiang Wang and the author. This is
further applied to formulate and establish for the first time the
Kazhdan-Lusztig theory for the BGG category $\mathcal{O}$ of the
ortho-symplectic Lie superalgebra $\mathfrak{osp}(2m|2n)$.
