The use of renewable sources for optical 3D printing instead of petroleum-based materials is increasingly growing. Combinations of photo- and thermal polymerization in dual curing processes can enhance the thermal and mechanical properties of the synthesized thermosets. Consequently, thiol-ene/thiol-epoxy polymers were obtained by combining UV and thermal curing of acrylated epoxidized soybean oil and epoxidized linseed oil with thiols, benzene-1,3-dithiol and pentaerythritol tetra(3-mercaptopropionate). Thiol-epoxy reaction was studied by calorimetry. The changes of rheological properties were examined during UV, thermal and dual curing to select the most suitable formulations for laser direct writing (LDW). The obtained polymers were characterized by dynamic-mechanical thermal analysis, thermogravimetry, and mechanical testing. The selected dual curable mixture was tested in LDW 3D lithography for validating its potential in optical micro- and nano-additive manufacturing. The obtained results demonstrated the suitability of epoxidized linseed oil as a biobased alternative to bisphenol A diglycidyl ether in thiol-epoxy thermal curing reactions. Dual cured thermosets showed higher rigidity, tensile strength, and Young’s modulus values compared with UV-cured thiol-ene polymers and the highest thermal stability from all prepared polymers. LDW results proved their suitability for high resolution 3D printing—individual features reaching an unprecedented 100 nm for plant-based materials. Finally, the biobased resin was tested for thermal post-treatment and 50% feature downscaling was achieved.