The influence of an electrically controlled biaxial in-plane strain on the magnetization of superlattices of ferromagnetic La0.7Sr0.3MnO3 and SrTiO3 was studied for single-layer thicknesses of d = 1.5-13 nm. Super-lattices were grown by pulsed laser deposition on both SrTiO3(001) and piezoelectric 0.72Pb(Mg1/3Nb2/3)O-3-0.28PbTiO(3)(001), or PMN-PT(001), substrates and have been structurally characterized by x-ray diffraction (XRD) and transmission electron microscopy. Grazing-incidence XRD reveals the vertical homogeneity of the piezoelectrically controlled reversible in-plane strain, even in a 600-nm-thick superlattice containing 100 oxide interfaces. The as-grown strain is almost identical in all superlattices that are coherently grown, with small variations resulting from the partially relaxed growth of the first La0.7Sr0.3MnO3 layer on PMN-PT(001). The magnetic transition temperature decreases with the layer thickness d as a consequence of the finite layer thickness, and the strain-induced response of the magnetization changes its character from that of a long-range-ordered ferromagnet to that of a magnetically disordered (possibly electronically phase-separated) manganite. The strain response of a modified interface layer ("dead layer") of the thickness d(I) is distinguished from that of the layer's interior by its different temperature dependence, allowing an estimation of 10 angstrom < d(I) < 16 angstrom for the superlattices on PMN-PT.