A thermodynamic cycle analysis is performed for refrigerator-precooled Linde-Hampson hydrogen liquefiers, including catalysts for the ortho-to-para conversion. Three different configurations of the liquefying system, depending upon the method of the o-p conversion, are selected for the analysis. After some simplifying and justifiable assumptions are made, a general analysis program to predict the liquid yield and the figure of merit (FOM) is developed with incorporating the commercial computer code for the thermodynamic properties of hydrogen. The discussion is focused on the effect of the two primary design parameters - the precooling temperature and the high pressure of the cycle. When the precooling temperature is in a range between 45 and 60 K, the optimal high pressure for the maximal liquid yield is found to be about 100 to 140 bar, regardless of the ortho-to-para conversion. However, the FOM can be maximized at slightly lower high pressures, 75 to 130 bar. It is concluded that the good performance of the precooling refrigerator is significant in the liquefiers, because at low precooling temperatures high values of the liquid yield and the FOM can be achieved without compression of gas to a very high pressure.