Texture-modified foods (TMFs) are essential for individuals with dysphagia, yet conventional formulations often lack structural consistency, nutritional density, and sensory appeal. Three-dimensional (3D) food printing offers new opportunities to tailor texture and composition. This study developed 3D-printed TMFs based on a lentil-carrot matrix and formulated with pea protein isolate (PPI), a curcumin-enriched oleogel (O), or their combination (PPI–O), and compared them with a commercial dysphagia thickener reference. Printability was assessed through extrusion force measurements and dimensional deviation analysis. Texture profile analysis (TPA), International Dysphagia Diet Standardisation Initiative (IDDSI) tests, moisture and protein content determination, color measurements, and preliminary sensory evaluation were conducted. PPI-containing formulations required higher extrusion forces but showed improved dimensional stability, hardness, cohesiveness, and gumminess compared with the oleogel-only sample, likely due to the formation of a stronger protein network. In contrast, the oleogel-only formulation exhibited lower mechanical resistance and a more pronounced melting perception, reflecting the lubricating effect of the lipid-based matrix. Protein content significantly increased with PPI incorporation, and curcumin-enriched oleogel also markedly influenced color parameters. All samples were classified as compatible with IDDSI Level 5. The hybrid PPI–O formulation provided a balanced combination of printability, structural fidelity, enhanced protein content, and suitable textural properties. These findings suggest that extrusion-based 3D printing may represent a promising approach for designing plant-based TMFs for dysphagia-oriented foods.