A note on Lefschetz fibrations on algebraic surfaces

Let $S$ be a smooth projective complex algebraic surface and $f, :, S, \longrightarrow, {\mathbb C}{\mathbb P}^2$ a finite map. Consider a pencil of hyperplane sections on $\mathbb{C}{\mathbb{P}}^2$ and pull it back to $S$. We address the question whether such a pencil is a Lefschetz pencil on $S$.