The replacement of mineral oils and non-renewable gelling agents is an imperative requirement for the lubricant industry in the near future. In this framework, cellulose pulp and castor oil are proposed as sustainable substitutes for these components. Biological treatment has been explored and evaluated to enhance the dispersing and thickening properties of cellulose pulp in oil media. Streptomyces sp. MDG147 and MDG301 strains were employed to modify agricultural wheat and barley straw residues from which cellulose pulp was obtained afterwards. In addition, an environmentally friendly process for the production of cellulose-pulp-/castor-oil-based polyurethanes was applied, in which neither catalysts nor harmful solvents were used, resulting in chemical oleogels. These oleogels were rheologically and tribologically characterized to evaluate their performance as lubricating greases. The enzymatic activity pattern developed was dependent on the raw material, the strain type, and the temperature, influencing the cellulose pulp’s composition, polymerization degree, and crystallinity. These modified characteristics tuned the rheological behavior of the different oleogels, providing a beneficial range of viscoelastic responses and viscosity values that were generally favored by the Streptomyces action. Furthermore, the friction coefficient and dimensions of wear scars measured in a tribological contact were comparable to, or even lower than, those found with commercial and other bio-based lubricating greases that have previously been studied.