In Paper I of this series (astro-ph/9911117) we described observations of 15 extragalactic targets taken with the Hubble Space Telescope GHRS/G160M grating for studies of the low-z Lya forest. We reported the detection of 110 Lya absorbers at significance level >3 sigma in the redshift range z=0.002-0.069, over a total pathlength of 116,000 km/s. In this second paper, we evaluate the physical properties of these Lya absorbers and compare them to their high-z counterparts. The distribution of Doppler parameters is similar to that at high redshift, with mean b = 35.0 +- 16.6 km/s. The true Doppler parameter may be somewhat lower, owing to component blends and non-thermal velocities. The distribution of equivalent widths exhibits a significant break at W~133mA, with an increasing number of weak absorbers (10mA-100mA). Adopting a curve of growth with b = 25 +- 5km/s and applying a sensitivity correction as a function of equivalent width and wavelength, we derive the distribution in column density, Nh^{-1.72+-0.06} for Nh<10^14 cm^-2. We find no redshift evolution in the sample at z<0.07, but we do see a significant decline in dN/dz compared to values at z>1.6. A 3 sigma signal in the two-point correlation function of Lya absorbers for velocity separations Delta v <150 km/s is consistent with results at high-z. Applying a photoionization correction, we find that the low-z Lya forest may contain ~20% of the total number of baryons, with closure parameter Omega_lya = (0.008+-0.001), for a standard absorber size and ionizing radiation field. Some of these clouds appear to be primordial matter, owing to the lack of detected metals in a composite spectrum. Our data suggest that a fraction of the absorbers are associated with gas in galaxy associations (filaments), while a second population is distributed more uniformly.
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