The development of new materials is currently focused on replacing fossil-based plastics with sustainable materials. Obtaining new bioplastics that are biodegradable and of the greenest possible origin could be a great alternative for the future. However, there are some limitations—such as price, physical properties, and mechanical properties—of these bioplastics. In this sense, the present work aims to explore the potential of lignin present in black liquor from paper pulp production as the main component of a new plastic matrix. For this purpose, we have studied the simple recovery of this lignin using acid precipitation, its thermoplastification with glycerin as a plasticizing agent, the production of blends with poly(caprolactone) (PCL), and finally the development of biocomposite materials reinforcing the blend of thermoplastic lignin and PCL with stone groundwood fibers (SGW). The results obtained show that thermoplastic lignin alone cannot be used as a bioplastic. However, its combination with PCL provided a tensile strength of, e.g., 5.24 MPa in the case of a 50 wt.% blend. In addition, when studying the properties of the composite materials, it was found that the tensile strength of a blend with 20 wt.% PCL increased from 1.7 to 11.2 MPa with 40 wt.% SGW. Finally, it was proven that through these biocomposites it is possible to obtain a correct fiber–blend interface.