  We obtain the conserved Abbott-Deser-Tekin (ADT)-{\it like} current for the
Lanczos-Lovelock gravity for a diffeomorphism vector, which defines the horizon
of a spacetime and, importantly, is not necessarily a Killing vector. As the
original ADT current is defined only for the presence of a background Killing
vector, one cannot use it extensively for the thermodynamic description of the
wide classes of non-Killing horizons which appear in gravity. On the other
hand, this general approach can be utilized for those horizons. Here, the
conserved current can be written as the derivative of the two-rank
anti-symmetric potential, the connection of which is apparent with the
conserved Noether potential from our analysis. If one assumes the
diffeomorphism vector as the Killing one, the results match to the ADT case,
whereas non-trivial result comes for the conformal Killing vectors and other
horizon defining diffeomorphism vectors.
