Liquid crystals displays with tailoring electrodes exhibit complex spatiotemporal dynamics when a large voltage is applied. We report experimental observations of the appearance of a programmable zig-zag lattice using an in-plane-switching cell filled with a nematic liquid crystal. Applying a small voltage to a wide range of frequencies, the system exhibits an Ising wall lattice. Increasing the voltage, this lattice presents a spatial instability generating an undulating wall lattice, and to higher voltages it becomes zig-zag type. Experimentally, we characterize the bifurcations and phase diagram of the wall lattice. Theoretically, we develop, from first principles, a descriptive model. This model has a good qualitative agreement with experimental observations.