We investigate connections between upper/lower estimates for Banach lattices and the notion of relative s-decomposability, which has roots in interpolation theory. To get a characterization of relatively s-decomposable Banach lattices in terms of the above estimates, we assign to each Banach lattice X two sequence spaces \(X_{U}\) and \(X_{L}\) that are largely determined by the set of p, for which \(l_{p}\) is finitely lattice representable in X. As an application, we obtain an orbital factorization of relative K-functional estimates for Banach couples \(\vec {X} =(X_{0},X_{1})\) and \(\vec {Y}=(Y_{0},Y_{1})\) through some suitable couples of weighted \(L_{{p}}\) -spaces provided if \(X_{i},Y_{i}\) are relatively s -decomposable for \(i=0,1\) . Also, we undertake a detailed study of the properties of optimal upper and lower sequence spaces \(X_{U}\) and \(X_{L}\) , and, in particular, prove that these spaces are rearrangement invariant. In the Appendix, a description of the optimal upper sequence space for a separable Orlicz space as a certain intersection of some special Musielak-Orlicz sequence spaces is given.
