  Understanding the strong interactions within baryonic systems beyond the up
and down quark sector is pivotal for a comprehensive description of nuclear
forces. This study explores the interactions involving hyperons, particularly
the $\Lambda$ particle, within the framework of nuclear lattice effective field
theory (NLEFT). By incorporating $\Lambda$ hyperons into the NLEFT framework,
we extend our investigation into the $S = -1$ sector, allowing us to probe the
third dimension of the nuclear chart. We calculate the $\Lambda$ separation
energies ($B_{\Lambda}$) of hypernuclei up to the medium-mass region, providing
valuable insights into hyperon-nucleon ($YN$) and hyperon-nucleon-nucleon
($YNN$) interactions. Our calculations employ high-fidelity chiral interactions
at N${}^3$LO for nucleons and extend it to $\Lambda$ hyperons with
leading-order S-wave $YN$ interactions as well as $YNN$ forces constrained only
by the $A=4,5$ systems. Our results contribute to a deeper understanding of the
SU(3) symmetry breaking and establish a foundation for future improvements in
hypernuclear calculations.
