  Conserved currents and related superpotentials for perturbations on arbitrary
backgrounds in the Lovelock theory are constructed. We use the Lagrangian based
field-theoretical method where perturbations are considered as dynamical fields
propagating on a given background. Such a formulation is exact (not
approximate) and equivalent to the theory in the original metric form. From the
very start, using Noether theorem, we derive the Noether-Klein identities and
adopt them for the purposes of the current work. Applying these identities in
the framework of Lovelock theory, we construct conserved currents,
energy-momentum tensors out of them, and related superpotentials with arbitrary
displacement vectors, not restricting to Killing vectors. A comparison with the
well known Abbott-Deser-Tekin approach is given. The developed general
formalism is applied to give conserved quantities for perturbations on anti-de
Sitter (AdS) backgrounds. As a test we calculate mass of the Schwarzschild-AdS
black hole in the Lovelock theory in arbitrary $D$ dimensions. Proposals for
future applications are presented.
