  We prove that every closed Bohr-Sommerfeld Lagrangian submanifold $Q$ of a
symplectic/K\"ahler manifold $X$ can be realised as a Morse-Bott minimum for
some 'convex' exhausting function defined in the complement of a
symplectic/complex hyperplane section $Y$. In the K\"ahler case, 'convex' means
strictly plurisubharmonic while, in the symplectic case, it refers to the
existence of a Liouville pseudogradient. In particular, $Q\subset X\setminus Y$
is a regular Lagrangian submanifold in the sense of Eliashberg-Ganatra-Lazarev.
