Some adaptations are permitted in the one reading and the response to the Word of God:
360. The reading of the word of God in the office for the dead proclaims the paschal mystery and conveys the hope of being gathered together again in God’s kingdom. The short reading in place in the hour or a longer Scripture reading from Part III (OCF 343-346) may be used (GILH 46). For pastoral reasons and if circumstance allow, a nonbiblical reading may be included at morning prayer or evening prayer in addition to the reading from Scripture, as is the practice in the office of readings.
361. A period of silence may follow the reading, then a brief homily based on the reading. After the homily the short reponsory or another responsorial song (see, for example (OCF) 403) may be sung or recited.
What sort of nonbiblical reading? Probably something from the saints.
Note that homily: brief, as in the Vigil liturgy.
Note that song: it could be a musical setting of the given responsory, or one of the texts from OCF 403 (remember these are songs of farewell, and other ritual texts). Option for recitation here, too. I suppose it is possible for a choir or cantor to sing something at this point. The assembly will join in the gospel canticle next.
I’ve been quizzed in St Blog’s a few times about the use of the sequence Dies Irae. If a traditionally-minded family asked, I suppose that I would counsel the use of this hymn as the “nonbiblical reading” at the office for the dead, and perhaps as the responsory after the homily. The caution is not to overshadow the proclamation of the Gospel text, which, in the hinge hours, is sung by those present.