  We study the topological entropy of the Lagrangian flow restricted to an
energy level $E_{L}^{-1}(c) \subset TM$ for $ c >e_0(L)$. We prove that if the
flow of the Tonelli Lagrangian $ L: M \to \mathbb{R}$, on a closed manifold of
dimension $ n+1$, has a non-hyperbolic closed orbit or an infinite number of
closed orbits with energy $ c>e_0(L)$ and satisfies certain open dense
conditions, then there exist a smooth potential $ u: M\to \mathbb{R} $, with $
C^2$-norm arbitrarily small, such that the flow of the perturbed Lagrangian $
L_u=L-u$ restricted to $E_{L_u}^{-1}(c)$ has positive topological entropy. The
proof of this result is based on an analog version of the Franks' Lemma for
Lagrangian flows and Ma\~n\'e's techniques on dominated splitting. As an
application, we show that if $\dim (M)=2$ and $c > e_0(L)$, then $ L$ admits a
$C^2$-perturbation by a smooth potential $u$, such that, the perturbed flow
$\phi_t^{L_u}\big{|}_{E_{L_u}^{-1}(c)}$ has positive topological entropy.
