Bio-based poly(lactic acid) (PLA) composite films were produced using unmodified soda micro- or nano-lignin as a green filler at four different contents, between 0.5 wt% and 5 wt%. The PLA–lignin composite polymers were synthesized by solvent casting to prepare a masterbatch, followed by melt mixing. The composites were then converted into films, to evaluate the effect of lignin content and size on their physicochemical and mechanical properties. Differential scanning calorimetry (DSC), supported by polarized light microscopy (PLM), infrared spectroscopy (FTIR-ATR), X-ray diffraction (XRD), and transmission electron microscopy (TEM) were employed to investigate the PLA crystallization and the interactions with Lignin (L) and Nanolignin (NL). The presence of both fillers (L and NL) had a negligible effect on the glass transition temperature (chain diffusion). However, it resulted in suppression of the corresponding change in heat capacity. This was indicative of a partial immobilization of the PLA chains on the lignin entities, due to interfacial interactions, which was slightly stronger in the case of NL. Lignin was also found to facilitate crystallization, in terms of nucleation; whereas, this was not clear in the crystalline fraction. The addition of L and NL led to systematically larger crystallites compared with neat PLA, which, combined with the higher melting temperature, provided indications of a denser crystal structure in the composites. The mechanical, optical, antioxidant, and surface properties of the composite films were also investigated. The tensile strength and Young’s modulus were improved by the addition of L and especially NL. The UV-blocking and antioxidant properties of the composite films were also enhanced, especially at higher filler contents. Importantly, the PLA–NL composite films constantly outperformed their PLA–L counterparts, due to the finer dispersion of NL in the PLA matrix, as verified by the TEM micrographs. These results suggest that bio-based and biodegradable PLA films filled with L, and particularly NL, can be employed as competitive and green alternatives in the food packaging industry.