  This paper is the second in a series aimed at examining the gaseous
environments of z$\le$0.3 quasars and ultraluminous infrared galaxies (ULIRGs)
as a function of AGN/host galaxy properties across the merger sequence. This
second paper focuses on the Ly$\alpha$ emission and O VI and N V absorption
features, tracers of highly ionized gas outflows, in ULIRGs observed with
HST/COS. Ly$\alpha$ emission is detected in 15 out of 19 ULIRGs, and 12 of the
14 clear Ly$\alpha$ detections show emission with blueshifted velocity
centroids and/or wings. The equivalent widths of the Ly$\alpha$ emission
increase with increasing AGN luminosities and AGN bolometric fractions. The
blueshifts of the Ly$\alpha$ emission correlate positively with those of the [O
III] emission, where the latter traces the ionized gas outflows. The Ly$\alpha$
escape fractions tend to be slightly larger in objects with stronger AGN and
larger outflow velocities, but they do not correlate with nebular line
reddening. Among the 12 ULIRGs with good continuum signal-to-noise ratios, O VI
and/or N V absorption features are robustly detected in 6 of them, all of which
are blueshifted, indicative of outflows. In the combined ULIRG $+$ quasar
sample, the outflows are more frequently detected in the X-ray weak or absorbed
sources. The absorption equivalent widths, velocities and velocity dispersions
of the outflows are also higher in the X-ray weak sources. No other strong
correlations are visible between the properties of the outflows and those of
the AGN or host galaxies.

Astrophysics of Galaxies;Cosmology and Nongalactic Astrophysics