The growing demand for sustainable materials has been driving research towards the use of biopolymers from natural resources. This study explores the valorization of lignin-rich solid residues derived from different eucalyptus wood conversion processes, specifically autohydrolysis (AHL), steam-explosion (SEL), and kraft pulping (EKL), via electrospinning. The potential of these electrospun nanostructures as eco-friendly oil structurant is investigated for lubricant applications. Solutions of AHL, SEL, and EKL fractions in a 3:1 v/v trifluoroacetic acid (TFA)/N,N-dimethylformamide (DMF) binary solvent were prepared at concentrations of 0.015, 0.03, and 0.05 g/mL. AHL and SEL samples exhibited superior spinnability due to higher carbohydrate content and molecular weight and lower ash content. Increasing the solution concentration to 0.05 g/mL resulted in the consecution of larger average fiber diameters (up to 0.44 and 0.39 μm, for AHL and SEL, respectively) and reduced bead formation. Stable oleo-dispersions were achieved solely with electrospun homogeneous nanofiber mats, while nanostructures predominantly composed of electrosprayed particles, like those obtained with EKL produced physically unstable dispersions from which the oil readily separates. The rheological response and microstructure of oleo-dispersions were significantly affected by both the conversion process of eucalyptus wood and the spinning solution concentration. The rheological properties of the oleo-dispersions can be tailored by modifying the spinning solution concentration, with G′ values ranging from 5·102 to 5·104 Pa and consistency and flow indices roughly ranging from 90 to 990 Pa sn and from 0.06 to 0.19, respectively, depending on the nature of the lignin-rich fraction and the type of electrospun nanostructure employed. These results highlight the potential of electrospun nanostructures obtained from lignin-rich solid residues in advanced materials applications, promoting the valorization of waste streams derived from different biorefinery processes, as well as the development of novel environmentally friendly lubricants.