  In literature, it is known that any solution of Painlev\'{e} VI equation
governs the isomonodromic deformation of a second order linear Fuchsian ODE on
$\mathbb{CP}^{1}$. In this paper, we extend this isomonodromy theory on
$\mathbb{CP}^{1}$ to the moduli space of elliptic curves by studying the
isomonodromic deformation of the generalized Lam\'{e} equation. Among other
things, we prove that the isomonodromic equation is a new Hamiltonian system,
which is equivalent to the elliptic form of Painlev\'{e} VI equation for
generic parameters. For Painlev\'{e} VI equation with some special parameters,
the isomonodromy theory of the generalized Lam\'{e} equation greatly simplifies
the computation of the monodromy group in $\mathbb{CP}^{1}$. This is one of the
advantages of the elliptic form.
