  In this paper, we will prove that the local time of a L\'evy process is of
finite $p$-variation in the space variable in the classical sense, a.s. for any
$p>2$, $t\geq 0$, if the L\'evy measure satisfies $\int_{R\setminus
\{0\}}(|y|^{3\over 2}\wedge 1)n(dy)<\infty$, and is a rough path of roughness
$p$ a.s. for any $2<p<3$ under a slightly stronger condition for the L\'evy
measure. Then for any function $g$ of finite $q$-variation ($1\leq q <3$), we
establish the integral $\int_{-\infty}^{\infty}g(x)dL_t^x$ as a Young integral
when $1\leq q<2$ and a Lyons' rough path integral when $2\leq q<3$. We
therefore apply these path integrals to extend the Tanaka-Meyer formula for a
continuous function $f$ if $\nabla ^-f$ exists and is of finite $q$-variation
when $1\leq q<3$, for both continuous semi-martingales and a class of L\'evy
processes.
