The magnetism of the second antiferromagnetic phase (AF2) arising in the iron-based LaFeAsO1-xHx superconductor for x≳0.4 was investigated by muon spin rotation measurements under hydrostatic pressure up to 2.6 GPa. The Néel temperature (TN) obtained for a sample with x=0.51 exhibits considerably greater sensitivity to pressure than that in the pristine antiferromagnetic phase (AF1; x≲0.06). Moreover, while the AF1 phase is always accompanied by the structural transition (from tetragonal to orthorhombic) at a temperature (Ts) which is slightly higher than TN, the AF2 phase prevails at higher pressures, above ∼1.5 GPa, where the structural transition is suppressed (Ts=0). These features indicate that the microscopic origin of the AF2 phase is distinct from that of AF1, suggesting that electronic correlation plays an important role in the former phase. We argue that the orbital-selective Mott transition is a plausible scenario to account for the observed pressure dependence of TN and Ts in the AF2 phase.