In this paper, we use large-angle, nearby galaxy redshift surveys to investigate the relationship between the 81 low-redshift Lyα absorbers in our HST/GHRS survey and galaxies, superclusters, and voids. In a subsample of 46 Lyα absorbers located in regions where the February 8, 2000 CfA catalog is complete down to at least L * galaxies, the nearest galaxy neighbors range from 100h −1 70 kpc to > 10h −1 70 Mpc. Of these 46 absorbers, 8 are found in galaxy voids. After correcting for pathlength and sensitivity, we find that 22 ± 8% of the Lyα absorbers lie in voids, which requires that at least some low-column density absorbers are not extended halos of individual bright galaxies. The number density of these clouds yields a baryon fraction of 4.5 ± 1.5% in voids.The stronger Lyα absorbers (10 13.2−15.4 cm −2 ) cluster with galaxies more weakly than galaxies cluster with each other, while the weaker absorbers (10 12.4−13.2 cm −2 ) are more randomly distributed. The median distance from a low-z Lyα absorber in our sample to its nearest galaxy neighbor (∼ 500h −1 70 kpc) is twice the median distance between bright galaxies in the same survey volume. This makes any purposed "association" between these Lyα absorbers and individual galaxies problematic. The suggested correlation between Lyα absorber equivalent width (W) and nearest-galaxy impact parameter does not extend to W ≤ 200 mÅ, or to impact parameters > 200h −1 70 kpc. Instead, we find statistical support for the contention that absorbers align with large-scale filaments of galaxies. The pair of sightlines, 3C 273 and Q 1230+0115, separated by 0.9 • on the sky, provides an example of 8 absorbers and 7 galaxies aligned along a possible filamentary structure at least 20h −1 70 Mpc long. While some strong (W > 400 mÅ) Lyα absorbers may be gas in the extended gaseous halos of individual galaxies, much of the local Lyα "forest" appears to be associated with the large-scale structures of galaxies and some with voids.