The numerical simulation of dynamic fracture in solids remains challenging due to the need to accurately capture crack initiation and propagation while maintaining robustness and mesh objectivity. Classical cohesive zone models (CZM) provide sharp crack representations well suited for post-fracture kinematics and contact, but they suffer from strong mesh dependence, where the underlying mesh significantly influences crack paths and fragment shapes, particularly in two- and three-dimensional simulations. Diffuse damage approaches, such as the Lip-field (LIP) approach, significantly reduce mesh dependence by enforcing spatial regularization of damage through a Lipschitz continuity constraint, yielding robust and mesh-objective crack patterns. However, the absence of explicit crack surfaces in the LIP-field approach complicates fragment identification and post-fracture interactions. The Cohesive Lipschitz (CLIP) model couples interface-based cohesive damage with a surrounding diffuse damage field obtained through a Lipschitz projection, enforcing Lipschitz continuity without introducing higher-order terms. This formulation retains explicit crack surfaces, facilitating post-fracture kinematics and contact, while significantly reducing sensitivity to mesh orientation. The model is constructed to be analytically equivalent to a linear cohesive law, ensuring physical consistency and allowing fracture energy to be redistributed in a controlled manner between cohesive interfaces and the bulk through a single regularization parameter. In this contribution, the CLIP formulation is assessed through a series of two-dimensional explicit dynamic benchmark problems, focusing on crack initiation, propagation, and interaction under dynamic loading. Standard benchmark configurations are considered to evaluate crack path prediction, mesh dependence, and energy dissipation. The results demonstrate that the CLIP model produces stable and mesh-robust crack trajectories while preserving the expected cohesive response and dynamic fracture characteristics. Comparisons with classical cohesive formulations highlight the improved robustness of the proposed approach in two dimensions. These results provide an important step toward the application of the CLIP model to large-scale dynamic fracture problems, confirming its suitability for two-dimensional simulations and its potential for extension to three-dimensional settings and more complex fracture modes.