Truss-based architected cellular materials offer a promising solution for shielding spacecraft from hypervelocity impacts (HVI) by micrometeoroids and orbital debris (MMOD). Numerical modelling plays a crucial role in developing these shields, as physical testing is resource intensive. Accurate contact modelling is essential for impact simulations, yet current finite element techniques like Lagrange multiplier and penalty methods can be computationally demanding or require extensive tuning. This study presents a novel momentum-based contact formulation for geometrically exact slender beams, avoiding the need for Lagrange multipliers and penalty parameters. A series of applications show that this new formulation effectively models low-velocity impacts and captures the contact stiffening effect, where strut self-contact in a collapsed lattice is reflected in the load response. The use of idealized pin joints for lattice modelling is nevertheless identified as a significant limitation. By advancing beam-to-beam contact modelling, this research supports the development of HVI shields and provides a foundation for future improvements.