  Using a recently proposed perturbative numerical renormalization-group
algorithm, we explore the connection between quantum criticality and the
emergence of Luttinger liquid physics in $t-J$ chains coupled by frustrated
interactions. This study is built on an earlier finding that at the maximally
frustrated point, the ground state of weakly-coupled Heisenberg chains is
disordered, the transverse exchanges being irrelevant. This result is extended
here to transverse couplings up to $J_{\perp}=0.6$, and we argue that it may
also be valid at the isotropic point. A finite size analysis of coupled
Heisenberg chains in the vicinity of the maximally frustrated point confirms
that the transverse spin-spin correlations decay exponentially while the
longitudinal ones revert to those of decoupled chains. We find that this
behavior persists upon moderate hole doping $x \alt 0.75$. For larger doping,
the frustration becomes inactive and the quantum critical point is suppressed.
