A series of polymer blends based on poly(lactic acid), PLA, and poly(3,3-ethylene dithiodipropionate) PEDPA, varying in the PLA/PEDPA ratio from 90/10 to 50/50, are studied in this work. The said systems are envisaged for transdermal drug carrier systems, moreover, to be prepared using the method of electrospinning and exhibiting self-healing capabilities. The study involves calorimetry, for glass transition and crystallization, and dielectric spectroscopy, for molecular dynamics, as the main investigation tools, supplemented by X-ray diffraction, polarized light and Fourier transform infrared spectroscopies. For comparison, we study neat PLA and PEDPA. Actually, for PEDPA, the local and segmental molecular mobility map is shown here for the first time. The two phases were found to affect each other's mobility, at a moderate extent. We conclude to the partial miscibility of the two polymers, resulting in systems with PLA matrices and PEDPA/PLA entities (drops) well dispersed throughout the matrix. The segmental dynamics of PLA accelerates in the blends, while the chain fragility (cooperativity) is suppressed, the effects indicating together a plasticization effect. On the other hand, the opposite results are recorded for the mobility of PEDPA at the presence of PLA, namely, deceleration and slight increase in fragility. Based on the ionic conductivity recordings, the PEDPA phase does not seem continuous throughout the blends' volume at any case of PEDPA fraction. In general, the crystallization of PLA is suppressed in the blends, in both the nucleation and crystalline fraction, and, subsequently, the melting point drops. Serious changes in the semicrystalline morphology are observed within the blends, in terms of smaller spherulites and of smaller density. Overall, the results suggest that the PLA/PEDPA blends offer potentials for tuning the macroscopic materials' performance, while the said combination of experimental techniques is able to provide useful information and indirect evidence regarding the polymers' topology.