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 $$\varLambda $$
Λ
particle, within the framework of nuclear lattice effective field theory (NLEFT). By incorporating $$\varLambda $$
Λ
hyperons into the NLEFT framework, we extend our investigation into the $$S = -1$$
S
=
-
1
sector, allowing us to probe the third dimension of the nuclear chart. We calculate the $$\varLambda $$
Λ
separation energies ($$B_{\varLambda }$$
B
Λ
) 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$$ ^3$$
3
LO for nucleons and extend it to $$\varLambda $$
Λ
hyperons with leading-order S-wave YN interactions as well as YNN forces constrained only by the $$A=4,5$$
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.