  The Lagrangian representation of multi-Hamiltonian PDEs has been introduced
by Y. Nutku and one of us (MVP). In this paper we focus on systems which are
(at least) bi-Hamiltonian by a pair $A_1$, $A_2$, where $A_1$ is a
hydrodynamic-type Hamiltonian operator. We prove that finding the Lagrangian
representation is equivalent to finding a generalized vector field $\tau$ such
that $A_2=L_\tau A_1$. We use this result in order to find the Lagrangian
representation when $A_2$ is a homogeneous third-order Hamiltonian operator,
although the method that we use can be applied to any other homogeneous
Hamiltonian operator. As an example we provide the Lagrangian representation of
a WDVV hydrodynamic-type system in $3$ components.
