Don’t forget our extended discussion of the funeral rites a decade ago. Also remember from our discussion of the Liturgy of the Hours: Psalms rule, and readings are usually a reflection on or a response to the psalms.
In OCF 389, the following rubric is given:
All are seated during the reading. The following reading or one of those provided in Part III … may be proclaimed by the reader.
The given text is brief, 1 Corinthians 15:55-57, an abbreviation of this choice. In the Office, a Gospel reading is not ordinarily proclaimed, and the readings are usually quite short, a few verses at most. Keep in mind that the Office for the Dead is chosenmore for the experience of praying the psalms and canticles. If a more direct encounter with prose readings is desired, then the Liturgy of the Word seems to be a better choice.
That reference to other readings in part III is covered in depth on this page.
More in red:
After the reading a period of silence may be observed; this may be followed by a brief homily.
Lay presiders at funeral vigils are not uncommon. I would be sure that most are capable preachers.
I suppose the instinct would be to offer words of remembrance here too. But the Office for the Dead makes the provision for this later in the liturgy.