No.
There is a long-standing tradition that comes from the Rule of Saint Benedict to only say the Lord’s Prayer (liturgically) 2 times per day at the Divine Office, i.e. at Lauds, and Vespers. The Mass makes up the third time. I’m not sure where this tradition of 3x per day comes from; the Rule only mentions the two times in the Divine Office.
In the Rule of Saint Benedict, in community prayer the practice at Compline (as well as the minor hours) is to say Kyrie Eleison-Christe Eleison-Kyrie Eleison; then the abbot, prior or presider intones “Pater Noster…”; then all recite the Lord’s Prayer in secret, until the presider says after an appropriate pause “et ne nos inducas in tentationem”, to which all reply “sed libera nos a malo”.
The reformed Roman Office (the LOTH), has not retained the Kyrie; one simply does not recite aloud the Lord’s Prayer at the Office of Readings, the daytime hours, or Compline.