  The properties of $\Lambda$-hyperons in pure $\Lambda$ matter are studied
with the finite-density QCD sum rule approach. The first order quark and gluon
condensates in $\Lambda$ nuclear matter are deduced from the chiral
perturbation theory. The sum rule predictions are sensitive to the four-quark
condensates, $<\bar{q}q>^2_{\rho}$ and $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$,
and the $\pi N$ sigma term. When $<\bar{q}q>^2_{\rho}$ is nearly independent of
density and $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$ depends strongly on density,
we can obtain weakly attractive $\Lambda$$\Lambda$ potentials (about several
MeV) in low $\Lambda$ density region, which agree with the information from the
latest double $\Lambda$ hyper-nucleus experiments. The nearly no density
dependence of $<\bar{q}q>^2_{\rho}$ and strong density dependence of
$<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$ can be explained naturally if the
properties of $<\bar{q}q>^2_{\rho}$ and $<\bar{q}q>_{\rho}<\bar{s}s>_{\rho}$
are assumed to be similar to those of $\pi\pi$ and $\bar{K} K$ in nuclear
medium, respectively.
