Fibonacci cubes and Lucas cubes have been studied as alternatives for the
classical hypercube topology for interconnection networks.
These families of graphs have interesting graph theoretic and enumerative properties.
Among the many generalization of Fibonacci cubes are $k$-Fibonacci cubes,
which have the same number of vertices as Fibonacci cubes, but
the edge sets determined by a parameter $k$. In this work, we consider $k$-Lucas cubes,
which are obtained as subgraphs of $k$-Fibonacci cubes
in the same way that Lucas cubes are obtained from Fibonacci cubes.
We obtain a useful decomposition property of $k$-Lucas cubes which allows for the calculation of
basic graph theoretic properties of this class, such as the number of edges, the average degree of a vertex,
the number of hypercubes they contain, the diameter and the radius.