  In the work of Rostami et al., the Bogomolov multiplier of a Lie algebra $L$
over a field $\Omega$ is defined as a particular factor of a subalgebra of the
exterior product $L \wedge L$. If $L$ is finite dimensional, we identify this
object as a certain subgroup of the second cohomology group $H^2(L, \Omega)$ by
deriving a Hopf-Type formula. As an application, we affirmatively answer two
questions posed by Kunyavskii regarding the invariance of the Bogomolov
multiplier under isoclinism of Lie algebras and the existence of a family of
Lie algebras with Bogomolov multipliers of unbounded dimension.
