Let f be is a binary string and d?1. Then the generalized Lucas cube Qd(f?)is introduced as the graph obtained from the Qd by removing all vertices that have a circulation containing f as a substring. The question for which f and d, the generalized Lucas cube Qd(f?) is an isometric subgraph of the d-cube Qd is solved for all binary strings of length at most five. Several isometrically embeddable and non-embeddable infinite series where f is of arbitrary length are given. Some structural properties of generalized Lucas cubes are also presented.