Using angle-resolved photoemission spectroscopy (ARPES), it is revealed that the low-energy electronic excitation spectra of highly underdoped superconducting and nonsuperconducting La2-xSrxCuO4 cuprates are gapped along the entire underlying Fermi surface at low temperatures. We show how the gap function evolves to a dx2-y2 form with increasing temperature or doping, consistent with the vast majority of ARPES studies of cuprates. Our results provide essential information for uncovering the symmetry of the order parameter(s) in strongly underdoped cuprates, which is a prerequisite for understanding the pairing mechanism and how superconductivity emerges from a Mott insulator.