We study the temperature dependence of the electrical resistivity in a system composed of critical spin chains interacting with three dimensional conduction electrons and driven to criticality via an external magnetic field. The relevant experimental system is Yb2Pt2Pb, a metal where itinerant electrons coexist with localized moments of Yb-ions which can be described in terms of effective S = 1/2 spins with dominantly one-dimensional exchange interaction. The spin subsystem becomes critical in a relatively weak magnetic field, where it behaves like a Luttinger liquid. We theoretically examine a Kondo lattice with different effective space dimensionalities of the two interacting sub-systems. We characterize the corresponding non-Fermi liquid behavior due to the "local criticality" from the spins by calculating the electronic relaxation rate and the dc resistivity and establish its quasi linear temperature dependence.