We present carbon nanotube (CNT)-reinforced polypropylene random copolymer (PPR) nanocomposites for the additive manufacturing of self-sensing piezoresistive materials via fused filament fabrication. The PPR/CNT feedstock filaments were synthesized through high shear-induced melt blending with controlled CNT loading up to 8 wt % to enable three-dimensional (3D) printing of nanoengineered PPR/CNT composites. The CNTs were found to enhance crystallinity (up to 6%) in PPR-printed parts, contributing to the overall CNT-reinforcement effect that increases both stiffness and strength (increases of 56% in modulus and 40% in strength at 8 wt % CNT loading). Due to electrical conductivity (∼10^–4–10^–1 S/cm with CNT loading) imparted to the PPR by the CNT network, multifunctional in situ strain and damage sensing in 3D-printed CNT/PPR bulk composites and lattice structures are revealed. A useful range of gauge factors (k) is identified for strain sensing (k_s = 10.1–17.4) and damage sensing (k_d = 20–410) across the range of CNT loadings for the 0° print direction. Novel auxetic re-entrant and S-unit cell lattices are printed, with multifunctionality demonstrated as strain- and damage-sensing in tension. The PPR/CNT multifunctional nanocomposite lattices demonstrated here exhibit tunable strain and damage sensitivity and have application in biomedical engineering for the creation of self-sensing patient-specific devices such as orthopedic braces, where the ability to sense strain (and stress) can provide direct information for optimization of brace design/fit over the course of treatment.