Given the declining demand for newsprint and the rising demand for packaging materials, new applications for high-yield pulps (HYPs), such as sustainable packaging, are being developed. While the traditional use of HYPs as a major component in paperboard is growing alongside this demand, their use in other packaging types with different property demands requires quality modifications or improvements to enhance mechanical strength and/or barrier properties. The research presented here explores the role of lignin and lignin-rich fine content, combined with hot-press technology, in improving the paper produced with chemithermomechanical pulp (CTMP). Critical properties for some packaging materials, as tensile strength (dry and wet) and air permeability were evaluated. Results indicate that moderate delignification (15%) or increased fines content together with hot-pressing improves the evaluated properties. The highest dry tensile strength was achieved through soft delignification, tripling the resistance (from 27 to 83 kN m/kg). Maximum wet strength (28 kN m/kg) was obtained with 35% fines content and 260 °C hot-pressing, which also resulted in the densest sheets. Air permeability was significantly reduced, either through partial delignification or by increasing the fines content, resulting in values decreasing from approximately 2000–20 mL/min. This approach aims to develop more sustainable packaging materials without relying on wet strength additives typically derived from fossil raw materials.