We present deep near-infrared observations of a dense region of the Lupus 3 cloud obtained with the ESO NTT and VLT. Using the NICE method, we construct a detailed high angular resolution dust extinction map of the cloud. The dust extinction map reveals embedded globules, a dense filament, and a dense ring structure. We derive dust column densities and masses for the entire cloud and for the individual structures therein. We construct radial extinction profiles for the embedded globules and find a range of profile shapes from relatively shallow profiles for cores with low peak extinctions, to relatively steep profiles for cores with high extinction. Overall, the profiles are similar to those of pressure-truncated isothermal spheres of varying center-to-edge density contrast. We apply Bonnor-Ebert analysis to compare the density profiles of the embedded cores in a quantitative manner and derive physical parameters such as temperatures, central densities, and external pressures. We examine the stability of the cores and find that two cores are likely stable and two are likely unstable. One of these latter cores is known to harbor an active protostar. Finally, we discuss the relation between an emerging cluster in the Lupus 3 cloud and the ring structure identified in our extinction map. Assuming that the ring is the remnant of the core within which the cluster originally formed, we estimate that a star formation efficiency of ~30% characterized the formation of the small cluster. Our observations of the Lupus 3 cloud suggest an intimate link between the structure of a dense core and its state of star-forming activity. The dense cores in this cloud are found to span the entire range of evolution from a stable, starless core of modest central concentration, to an unstable, star-forming core that is highly centrally concentrated, to a significantly disrupted core from which a cluster of young stars is emerging.

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