Important exceptions to the four-week cycle:
134. On solemnities and feasts, during the Easter triduum, and on the days within the octaves of Easter and Christmas, proper psalms are assigned to the office of readings from those with a tradition of use at these times and their relevance is generally highlighted by the choice of antiphon. This is also the case at daytime prayer on certain solemnities of the Lord and during the octave of Easter. At morning prayer the psalms and canticle are taken from the Sunday of the Week I of the psalter. On solemnities the psalms at evening prayer I are taken from the Laudate Psalms, following an ancient custom. At evening prayer II on solemnities and at evening prayer on feasts the psalms and canticle are proper. At daytime prayer on solemnities (except those already mentioned and those falling on Sunday) the psalms are taken from the Gradual Psalms; at daytime prayer on feasts the psalms are those of the current week and day of the psalter.
The Laudate Psalms are 148, 149, and 150. The Gradual Psalms are 120-134.
135. In all other cases the psalms are taken from the current week and day of the psalter, unless there are proper antiphons or proper psalms.
An ordo or liturgical calendar will dispense of the need to be a do-it-yourself-liturgist on these things. Take it from a liturgist who has missed a major feast or two in a bad way once or twice. There is an e-ordo available here. Don’t forget that each diocese and parish may have exceptions to the general calendar. The dedication anniversary of your cathedral and your parish are two feasts that might (and should) affect the LH even if it is prayed in the home.