"4. The Litany may replace the prayers in the Daily Office (Matins, Vespers, Morning Prayer, Evening Prayer) or the General Prayer in the Divine Service. It may also serve as an entrance rite in the Divine Service, replacing the Introit, Kyrie, and Hymn of Praise." Lutheran Service Book Altar Book, p. 410
If combined with rubric 6, that it is especially appropriate for penitential times, whether seasons (Advent and Lent) or days (Wednesday, Fridays, Days of Repentance and Prayer), it would seem to lend itself to the possibility of using the Litany in the Passion Vespers of Lent and the Prayer of the Church during at least some of the Sundays of Lent. A good time to teach the singing of this prayer - rather easy and hauntingly beautiful.