The General Instructions on the Liturgy of the Hours provides the following regarding Memorials and Commemorations during privileged seasons (emphasizes added to highlight relevance during Lent):
237. On Sundays, solemnities, and feasts, on Ash Wednesday, during Holy Week, and during the octave of Easter, memorials that happen to fall on these days are disregarded.
238. On the weekdays from 17 to 24 December, during the octave of Christmas, and on the weekdays of Lent, no obligatory memorials are celebrated, even in particular calendars. When any happen to fall during Lent in a given year, they are treated as optional memorials.
239. During privileged seasons, if it is desired to celebrate the office of a saint on a day assigned to his or her memorial:
a. in the office of readings, after the patristic reading (with its responsory) from the Proper of Seasons, a proper reading about the saint (with its responsory) may follow, with the concluding prayer of the saint;
b. at morning prayer and evening prayer, the ending of the concluding prayer may be omitted and the saint’s antiphon (from the proper or common) and prayer may be added.
In practice what this means is that memorials and commemorations during Lent, because it is a privileged season, are all treated as optional commemorations regardless of their status in the calendar. You will notice if you own a four-volume Liturgy of the Hours set that all of the memorials in the Proper of the Saints within volume II for the Lent/Easter season are called commemorations and the reading provided for the Office of Readings is given the heading “Reading” vice “Second Reading” and this related to the rubrics above. During privileged seasons like Lent, memorials are not just downgraded, they are observed differently within the Hours themselves. In fact, their observance is more traditional and reflect the previous Breviary formula of commemorating memorials and feasts that fell on the same day during the year.
When putting together your Hours and ribbons for the day during Lent you have a few considerations during days when there is an optional memorial for a Saint. First, you may decided not to proceed with the commemoration at all. This is a perfectly valid option during any privileged season and if it is the case you simply carry on with the proper parts from the weekday/Sunday for the season without any regard for the Proper of Saints or additional readings/prayers. Second, you may decide to mark the commemoration and if this is the case you can decided to do so during the Office of Readings or Morning/Evening Prayer (any combination or both) or at all of the these offices.
If you are marking the commemoration during the Office of Readings you add the reading related to the Saint and the responses from the Proper of Saints to the First and Second reading from the Proper of the Seasons. So on that day your Office of Readings will have an Old Testament reading, a patristic reading from a church father or other source, and a third reading related to the particular Saint each with their own responses from the respective proper. For the closing prayer, you will disregard the prayer in the Proper of the Seasons and will close with the prayer from the Proper of Saints.
If you are marking the commemoration during Morning/Evening Prayer you add the Gospel Canticle antiphon at the very end of the Collect from the Proper of the Seasons as well as the Collect for that particular Saint just before ending the Office. This is an old practice that was once very common in the older forms of the Divine Office but is now out of use save for during periods of privileged seasons.
And again, you have the option of either not observing the memorial at all, or of observing it during the Office of Readings or Morning/Evening Prayer or both. The rubrics provide for these options. I would say that when possible you should observe the commemoration during at least one of the Hours during the day. If you have more time than all of the Hours is best. With the option of merely adding the antiphon and prayer at the end of Morning/Evening Prayer, one is not really increasing the prayer load any more during the season. Plus, there is nothing wrong with adding a little bit more of a burden to your prayer life during Lent— just saying.
Remember this does not apply to feasts or solemnities— those retain their same status and format during any season. We can take a quick look at how the commemorations change the Liturgy of the Hours for the day.
For example, today is the memorial of Polycarp, Bishop and Martyr. In the calendar this is a Memorial and would not be optional. However, in the Proper of Seasons (LOTH Vol II, p. 1694) it is labelled as a commemoration and this is because of instruction 238 above (if you look up the same Saint in another volume of the LOTH you’ll notice the heading will say Memorial and the reading provided for the Office of Readings will have the heading Second Reading instead of just Reading– this is a good indication to you when planning what has to happen during the Office itself). Today is Tuesday of the First Week of Lent (LOTH Vol II, p. 102) and the first reading after the psalms and antiphons (from the four-week psalter) is Exodus 6:29-7:25, the second reading is from a treatise on the Lord’s Prayer by Saint Cyprian and (if I am observing the commemoration during this Office) a third, additional, reading will come from the Proper of the Saints for Polycarp which is a letter on his martyrdom by the Church of Smyrna. After I completed all three reading with their responsories, I would end the Office of Readings with the prayer related to Polycarp found on page 1697 of the Liturgy of the Hours Vol II book.
The format for Morning/Evening prayer is a little different however. You would still reference the Gospel Canticle antiphon found on page 1697 of the Liturgy of the Hours Vol II book for Polycarp but this would be added immediately following the closing prayer from the Office in accordance with the Proper of the Seasons. So you would complete nearly the entire Office as it should be done for the day and right at end the end of the daily prayer, instead of closing with “We ask this though…” you would recite the Gospel Canticle antiphon related to Polycarp (either the one for the Cantle of Zechariah or of Mary depending it being morning or evening) and then you would recite his prayer and close with the typical “We ask this through…”. And that would be it.