n this work, we study the possibility of realizing two distinct mechanisms of metal-insulator transitions in hole-doped cuprates induced by the localization of charge carriers near the small-radius impurities and in a deformable lattice (i.e. in the absence of impurities). The purpose of this research is to determine the criteria (i.e. conditions) for the existence of the localized states of hole carriers and solve the problem of metal-insulator transitions in La-based cuprates. The advantage of La-based cuprate versus other types of cuprates is that two distinct metal-insulator transitions in La-based cuprates driven by the strong carrier-impurity-phonon and carrier-phonon interactions occur simultaneously in a wider doping range from the lightly doped to heavily doping regime. We show that at very low doping, the separate levels of hole carriers localized near impurities and in a deformable lattice are formed in the charge-transfer gap of the cuprates. As the doping level increases towards underdoped region, the energy levels of such charge carriers start to form energy bands which gradually broaden with increasing doping. We propose a new two-carrier cuprate superconductor model for studying two distinct metal-insulator transitions occurring simultaneouslyin hole-doped La-based cuprate compounds. We demonstrate that when hole carriers reside in impurity and polaron bands, these metal-insulator transitions in La-based superconductors with small-radius dopants occur accordingly in a wide doping range and relatively lower doping levels.