Bio-based adhesives have been largely applied on several applications in many industrial areas, including automotive and laminated food packaging. Polyurethanes (PU) occupy a leading position among the most used bio-based polymers due to their large range of properties and application versatility. Recent works reported that PU obtained from castor oil and Kraft lignin as polyol developed high mechanical properties and blend miscibility. In spite of its well-known mechanical behavior, additional investigations might support the application of this bio-based PU as adhesive. In this context, our work investigated the effect of adhesive (bondline) thickness variation (size effect) on shear modulus of a bio-based polyurethane under finite deformation and related shear stress distribution. Polyurethane was obtained using a blend of Kraft lignin and castor oil as polyol (20 wt% of Kraft lignin) and applied as adhesive for metal bonding, in which adhesive thickness changed from tens of micrometers up to 220 micrometers. Steel plates were used as substrates and adhesive shear modulus was evaluated using substrates with large thickness (4.76 mm), which minimized the effect of substrate deformation on shear modulus measurement. Single lap joints were uniaxial loaded in order to generate the shear stress on adhesive bondline. Additionally, shear modulus changes were simulated by finite element analysis (FEA), analytical models and compared to experimental data. Results revealed the size effect and pointed to high shear modulus of the PU bondline, justifying its use as an adhesive for structural applications.