  This is the fourth of a series of papers on low X-ray luminosity galaxy
clusters. The sample comprises 45 galaxy clusters with X-ray luminosities
fainter than 0.7 10$^{44}$ erg s$^{-1}$ at redshifts lower than 0.2 in the
regions of the Sloan Digital Sky Survey. The sample of spectroscopic members of
the galaxy clusters was obtained with the criteria: r$_p$ $\le$ 1 Mpc and
$\Delta V \leq \sigma$ using our $\sigma$ estimates containing 21 galaxy
clusters with more than 6 spectroscopic members. We have also defined a sample
of photometric members with galaxies that satisfy r$_p \le $ 1 Mpc, and $\Delta
V \leq $ 6000 \kms including 45 galaxy clusters with more than 6 cluster
members.
  We have divided the redshift range in three bins: $z \leq 0.065$; 0.065 $<$ z
$<$ 0.10; and z $\ge$ 0.10. We have stacked the galaxy clusters using the
spectroscopic sub-sample and we have computed the best RS linear fit within
1$\sigma$ dispersion. With the photometric sub-sample, we have added more data
to the RS obtaining the photometric 1$\sigma$ dispersion relative to the
spectroscopic RS fit. We have computed the luminosity function using the
$1/V_{max}$ method fitting it with a Schechter function. The obtained
parameters for these galaxy clusters with low X-ray luminosities are remarkably
similar to those for groups and poor galaxy clusters at these lower redshifts.
