We address the Λ hypernuclear "overbinding problem" in light hypernuclei which stands for a 1-3 MeV excessive Λ separation energy calculated in _{Λ}^{5}He. This problem arises in most few-body calculations that reproduce ground-state Λ separation energies in the lighter Λ hypernuclei within various hyperon-nucleon interaction models. Recent pionless effective field theory (πEFT) nuclear few-body calculations are extended in this work to Λ hypernuclei. At leading order, the ΛN low-energy constants are associated with ΛN scattering lengths, and the ΛNN low-energy constants are fitted to Λ separation energies (B_{Λ}^{exp}) for A≤4. The resulting πEFT interaction reproduces in few-body stochastic variational method calculations the reported value B_{Λ}^{exp}(_{Λ}^{5}He)=3.12±0.02  MeV within a fraction of MeV over a broad range of πEFT cutoff parameters. Possible consequences and extensions to heavier hypernuclei and to neutron-star matter are discussed.