  We continue exploring our understanding of the collective properties of X-ray
binaries in the stellar fields (i.e., outside globular clusters) of normal
galaxies, introduced in Paper I of this series, where we considered high-mass
X-ray binaries (HMXBs). In this paper (Paper II of the series) and the
companion paper (Paper III of the series), we consider low-mass X-ray binaries
(LMXBs), whose evolutionary scenario is very different from that of HMXBs. In
this paper, we consider the evolution of primordial binaries upto the stage
where the neutron star just formed in the supernova explosion of the primary is
in a binary with its low-mass unevolved companion, and this binary has
circularized tidally, producing what we call a pre-low-mass X-ray binary
(pre-LMXB). We study the constraints on the formation of such pre-LMXBs in
detail (since these are low probability events), and calculate their collective
properties and formation rate. To this end, we first consider the changes in
the binary parameters in the various steps involved, viz., the common-envelope
(CE) phase, the supernova, and the tidal evolution. This naturally leads to a
clarification of the constraints. We then describe our calculation of the
evolution of the distributions of primordial binary parameters into those of
the pre-LMXB parameters, following the standard evolutionary scenario for
individual binaries. We display the latter as both bivariate and monovariate
distributions, discuss their essential properties, and indicate the influence
of some essential factors on these. Finally, we calculate the formation rate of
pre-LMXBs. The results of this paper are used in the next one (Paper III) to
compute the expected X-ray luminosity function (XLF) of LMXBs, which is
compared with observation.
