The correlation functions of $p\Xi^-$ and $\Lambda\Lambda$ pairs
from $pp$ and $pA$ collisions
are studied in the coupled-channel framework
using the $N\Xi\text{-}\Lambda\Lambda$ coupled-channel baryon-baryon
potentials obtained in the lattice QCD calculation at almost physical quark masses.
The $p\Xi^-$ correlation function is calculated to be significantly enhanced
from the pure Coulomb case,
while the $\Lambda\Lambda$ correlation function is slightly enhanced
from that of the pure Fermion quantum statistics.
These features reflect the large and small scattering lengths
in the $p\Xi^-$ and $\Lambda\Lambda$ channels in magnitude,
and agree with the observed data by the ALICE collaboration.
The agreement confirms the $S=-2$ baryon-baryon potentials from lattice QCD.