The origin of life must have involved an unlikely transition from chaotic chemistry to reproducing supramolecular structures. Previous quantitative analyses of reproducing mutually catalytic networks made of simple molecules have led to increasing popularity of this pre-RNA scenario for life’s origin. Here, we investigate in detail the reproduction characteristic of the GARD computer-simulated physicochemically rigorous lipid-based model. This model displays compatibility with heterogeneous environments, addresses the network’s spatial demarcation, and portrays trans-generational compositional information transfer. However, we find that compositionally reproducing states are extremely rare, suggesting that random roaming would be a vastly inefficient path towards reproduction. Rewardingly, further scrutiny shows that all self-reproducing states are also dynamic attractors of the catalytic network. This suggests a greatly enhanced propensity for the spontaneous emergence of reproduction and primal evolution, vastly augmenting the likelihood of protolife appearance.