Cell membranes are one of the main targets of oxidative processes mediated by reactive oxygen species (ROS). These chemical species interact with unsaturated fatty acids of membrane lipids, triggering an autocatalytic chain reaction, producing lipid hydroperoxides (LOOHs) as the first relatively stable product of the ROS-mediated lipid peroxidation (LPO) process. Numerous biophysical and computational studies have been carried out to elucidate the LPO impact on the structure and organization of lipid membranes. However, although LOOHs are the major primary product of LPO of polyunsaturated fatty acids (PUFAs), to the best of our knowledge, there is no experimental evidence on the effects of the accumulation of these LPO byproducts on the electrical properties and the underlying dynamics of lipid membranes. In this work, bilayer lipid membranes (BLMs) containing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocoline (POPC) with increasing hydroperoxidized POPC (POPC-OOH) molar proportions (BLMPC/PC-OOH) are used as model membranes to investigate the effect of LOOH-mediated LPO propagation on the electrical behavior of lipid bilayers. Voltage-induced ion current signals are analyzed by applying the fractal method of power spectrum density (PSD) analysis. We experimentally prove that, when certain LOOH concentration and energy threshold are overcome, oxidized membranes evolve toward a critical state characterized by the emergence of non-linear electrical behavior dynamics and the pore-type metastable structures formation. PSD analysis shows that temporal dynamics exhibiting "white" noise (non-time correlations) reflects a linear relationship between the input and output signals, while long-term correlations (β > 0.5) begin to be observed closely to the transition (critical point) from linear (Ohmic) to nonlinear (non-Ohmic) behavior. The generation of lipid pores appears to arise as an optimized energy dissipation mechanism based on the system's ability to self-organize and generate ordered structures capable of dissipating energy gradients more efficiently under stressful oxidative conditions.