  We consider measurable $F: \Omega \times \mathbb{R}^d \to \mathbb{R}$ where
$F(\cdot, x)$ belongs for any $x$ to the Malliavin Sobolev space
$\mathbb{D}_{1,2}$ (with respect to a L\'evy process) and provide sufficient
conditions on $F$ and $G_1,\ldots,G_d \in \mathbb{D}_{1,2}$ such that $F(\cdot,
G_1,\ldots,G_d) \in \mathbb{D}_{1,2}.$
  The above result is applied to show Malliavin differentiability of solutions
to BSDEs (backward stochastic differential equations) driven by L\'evy noise
where the generator is given by a progressively measurable function
$f(\omega,t,y,z).$
