  The $\Lambda$ separation energies in the mirror hypernuclei
${_{\Lambda}^4}{\rm H}-{_{\Lambda}^4}{\rm He}$ exhibit large charge symmetry
breaking (CSB). Analyzing this CSB within pionless effective field theory while
using partially conserved baryon-baryon SU(3) flavor symmetry, we deduce a
$\Lambda -\Sigma^0$ induced in-medium admixture amplitude ${\cal
A}_{I=1}\approx 1.5\%$ in the dominantly isospin $I=0$ $\Lambda$ hyperon. Our
results confirm the free-space value ${\cal A}^{(0)}_{I=1}$ inferred directly
within the SU(3) baryon octet by Dalitz and von-Hippel in 1964 and reaffirmed
in a recent QCD+QED lattice calculation. Furthermore, exploring the
consequences of SU(3) flavor symmetry on the $\Lambda$-nucleon interaction, we
find that CSB is expected to impact the $S=1$ and $S=0$ spin channels in
opposite directions, with the latter dominating by an order of magnitude. These
observations explain a recent deduction of $\Lambda$-nucleon CSB strengths.
