The category $\mathcal{O}$ is the category of all finitely generated, locally $\mathfrak{b}$-finite and $\mathfrak{h}$-semisimple $\mathfrak{g}$-modules, where $\mathfrak{g}$ is a complex semisimple Lie algebra with Cartan subalgebra $\mathfrak{h}$ and Borel subalgebra $\mathfrak{b}$ containing $\mathfrak{h}$.
Let $M(\lambda)$ be the Verma module with highest weight $\lambda$, $L(\lambda)$ be its unique simple quotient.
Does $\text{Ext}^i_{\mathcal{O}}(M(\lambda),M(\mu))=0$ imply that $\text{Ext}^i_{\mathcal{O}}(M(\lambda),L(\mu))=0$?
