Homogeneous and non-homogeneous Lizorkin-Triebel spaces with generalized smoothness ˙ F λ(.) pq (R n) and F λ(.) pq (R n) have been considered. In particular, under some assumptions of the function λ(t) : R + → R + , λ(1) = 1 determining the generalized smoothness properties, the discretization procedure is realized and the relationship is established between these spaces on R n and their discrete analogues.