  We investigate the effect of external pressure on magnetic order in undoped
LnFeAsO (Ln = La, Ce, Pr, La) by using muon-spin relaxation measurements and
ab-initio calculations. Both magnetic transition temperature $T_m$ and Fe
magnetic moment decrease with external pressure. The effect is observed to be
lanthanide dependent with the strongest response for Ln = La and the weakest
for Ln = Sm. The trend is qualitatively in agreement with our DFT calculations.
The same calculations allow us to assign a value of 0.68(2) $\mu_B$ to the Fe
moment, obtained from an accurate determination of the muon sites. Our data
further show that the magnetic lanthanide order transitions do not follow the
simple trend of Fe, possibly as a consequence of the different $f$-electron
overlap.
