In this paper we present measurements of velocity dispersions and Lick indices for 509 galaxies in the local universe, based on high signal-to-noise, long-slit spectra obtained with the 1.52 m ESO telescope at La Silla. The conversion of our measurements into the Lick/IDS system was carried out following the general prescription of Worthey & Ottaviani in 1997. Comparisons of our measurements with those of other authors show, in general, good agreement. We also examine the dependence between these indices (e.g., Hβ, Mg₂, Fe5270, and NaD) and the central velocity dispersion (σ₀), and we find that they are consistent with those previously reported in the literature. Benefiting from the relatively large size of the sample, we are able to investigate the dependence of these relations on morphology and environment, here represented by the local galaxy density. We find that for metallic lines these relations show no significant dependence on environment or morphology, except in the case of NaD, which shows distinct behavior for E and S0. On the other hand, the Hβ-log σ₀ shows a significant difference as a function of the local density of galaxies, which we interpret as being caused by the truncation of star formation in high-density environments. Comparing our results with those obtained by other authors, we find a few discrepancies, adding to the ongoing debate about the nature of these relations. Finally, we report that the scatter of the Mg indices versus σ₀ relations correlates with Hβ, suggesting that age may contribute to the scatter. Furthermore, this scatter shows no significant dependence on morphology or environment. Our results are consistent with the currently popular downsizing model, where low-mass galaxies have an extended star-formation history, except for those located in high-density regions.