Doping a "parent" antiferromagnetic Mott insulator in cuprates leads to short-range electronic correlations and eventually to high-Tc superconductivity. However, the nature of charge correlations in the lightly doped cuprates remains unclear. Understanding the intermediate electronic phase in the phase diagram (between the parent insulator and the high-Tc superconductor) is expected to elucidate the complexity both inside and outside the superconducting dome, and in particular in the underdoped region. One such phase is ferroelectricity whose origin and relation to the properties of high-Tc superconductors is subject of current research. Here we demonstrate that ferroelectricity and the associated magnetoelectric coupling are in fact common in La-214 cuprates namely, La2-xSrxCuO4, La2LixCu1-xO4 and La2CuO4+x. It is proposed that ferroelectricity may result from local CuO6 octahedral distortions, associated with the dopant atoms and clustering of the doped charge carriers, which break spatial inversion symmetry at the local scale whereas magnetoelectric coupling can be tuned through Dzyaloshinskii-Moriya interaction.