The Hopf Boundary Point Lemma

http://en.wikipedia.org/wiki/Hopf_lemma

is a result for the unit normal vector field and the normal derivative.

Is it true if one considers arbitrary directional derivative? Let

$$ l : \partial \Omega \rightarrow \mathbb R^n$$ be a differentiable unit vector field. My question is if under the same conditions we have for the directional derivative $$\frac{\partial u}{\partial l} (x_0) > 0$$

Any reference is appreciated.