Part IV of the Order of Christian Funerals gives instruction, rubrics and other texts for the Office for the Dead. For an in-depth discussion of the Liturgy of the Hours, I refer readers here to the archives under the category “GILH” (the General Introduction to the Liturgy of the Hours).
We’ll take a bit of time with the OCF sections 348 through 396. Maybe you’ll be convinced that the Liturgy of the Hours is a sound way for the faith community to celebrate some aspect of a believer’s funeral.
348. The vigil for the deceased may be celebrated in the form of some part of the office for the dead. To encourage this form of the vigil, the chief hours, “Morning Prayer” and “Evening Prayer,” are provided here. When the funeral liturgy is celebrated the evening before the committal, it may be appropriate to celebrate morning prayer before the procession to the place of committal.
The rite “encourages” the consideration of Lauds or Vespers. Vespers would be my personal preference for my own funeral vigil.
Catholic Sensibility 
At my father’s funeral at STA in 1999 we used a modified form of Compline as the wake service. It seemed to work – but that’s me, since I love Compline’s simplicity.
“Guide me waking, Lord, and guard me sleeping that awake I may watch with Christ and asleep I may rest in peace.”