  We study the role of major and minor mergers in the mass growth of luminous
red galaxies. We present small-scale ($0.01<r<8\,\hMpc$) projected
cross-correlation functions of $23043$ luminous early-type galaxies from the
Sloan Digital Sky Survey (SDSS) Luminous Red Galaxy (LRG) sample
($0.16<z<0.30$, $\MMi\approx -22.75\,\mag$) with all their companions in the
SDSS imaging sample, split into color and luminosity subsamples with
$\MMi<-18\,\mag$. We de-project the two-dimensional functions to obtain
three-dimensional real-space LRG--galaxy cross-correlation functions for each
companion subsample. We find that the cross-correlation functions are not
purely power-law and that there is a clear ``one-halo'' to ``two-halo''
transition near $1\,\hMpc$. We convert these results into close pair statistics
and estimate the LRG accretion rate from each companion galaxy subsample using
timescales from dynamical friction arguments for each subsample of the
companions. We find that the accretion onto LRGs is dominated by dry mergers of
galaxies more luminous than $\Lstar$. We integrate the luminosity accretion
rate from mergers over all companion galaxy subsamples and find that LRGs are
growing by $[1.7\pm 0.1]$ percent per $\Gyr$, on average, from merger activity
at redshift $z\sim 0.25$. This rate is almost certainly an over-estimate
because we have assumed that all close pairs are merging as quickly as
dynamical friction allows; nonetheless it is on the low side of the panoply of
measurements in the literature, and lower than any rate predicted from theory.
