We investigate the effect of external pressure on magnetic order in undoped LnFeAsO (Ln=La, Ce, Pr, Sm) by using muon spin relaxation measurements and ab initio calculations. Both the magnetic transition temperature T_m and the 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 density functional theory calculations. The same calculations allow us to assign a value of 0.68(2) μ_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.