By making a systematic study of the hydrogen-doped LaFeAsO system by means of dc resistivity, dc magnetometry, and muon-spin spectroscopy, we addressed the question of universality of the phase diagram of rare-earth-1111 pnictides. In many respects, the behaviour of LaFeAsO1−xHx resembles that of its widely studied F-doped counterpart, with H− realizing a similar (or better) electron doping in the LaO planes. In an x = 0.01 sample we found a long-range spin-density wave (SDW) order with TN = 119 K, while at x = 0.05 the SDW establishes only at 38 K and, below Tc = 10 K, it coexists at a nanoscopic scale with bulk superconductivity. Unlike the abrupt magnetic-superconducting transition found in the La-1111 compound, the presence of a crossover region makes the H-doped system qualitatively similar to other Sm-1111, Ce-1111, and Nd-1111 families.