Magnetization measurements have been performed to understand the role of the magnetic structure on the superconducting properties of epitaxial thin films of Ba1-xLaxFe2As2(x= 0.08, 0.13, and 0.18) deposited on single crystal (001)-oriented MgO substrates by pulsed laser deposition. All samples exhibit a reentrant-spinglass like behavior at normal state. At lower temperatures, we observe the same magnetic state coexisting with superconductivity and it is also observed a prominent non-linear giant diamagnetism in an intermediate temperature range just above the superconducting phase transition temperature. Furthermore, no significant change in the magnetic domain structure was detected by the onset of superconductivity. Based on their magnetic states, we claim that each domain (as a disconnected superconducting island) has its own bulk superconducting properties. Finally, we discussed the dual character played by the La atoms in the superconducting properties. That duality character has been also confirmed by analyzing resistivity data.