  The magnetism of the second antiferromagnetic phase (AF2) arising in the
iron-based LaFeAsO$_{1-x}$H$_{x}$ superconductor for $x\gtrsim0.4$ was
investigated by muon spin rotation measurements under hydrostatic pressure up
to 2.6 GPa. The N\'eel temperature ($T_{\rm N}$) obtained for a sample with
$x=0.51$ exhibits considerably greater sensitivity to pressure than that in the
pristine antiferromagnetic phase (AF1, $x\lesssim0.06$). Moreover, while the
AF1 phase is always accompanied by the structural transition (from tetragonal
to orthorhombic) at a temperature ($T_{\rm s}$) which is slightly higher than
$T_{\rm N}$, the AF2 phase prevails at higher pressures above $\sim$1.5 GPa
where the structural transition is suppressed ($T_{\rm s}=0$). These features
indicate that the microscopic origin of the AF2 phase is distinct from that of
AF1, suggesting that electronic correlation plays 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 $T_{\rm N}$ and
$T_{\rm s}$ in the AF2 phase.
