Some structural and enumerative properties of the Lucas cubes are determined in this paper. More precisely, these properties are the independence numbers of the edges and vertices, the radius, the center of the generating function of a sequence of numbers connected to the partite sets, the asymptotic behavior of the ratio of the numbers of edges and vertices. Some identities involving Fibonacci and Lucas numbers are obtained. The Lucas semilattices are introduced and their characteristic polynomials are found.