Gordon Wenham gives four theological reasons for using lament psalms (with slight modification).
1. The lament psalms are some of the most quoted in the New Testament.
2. Jesus prayed the lament psalms.
3.The martyr’s prayers in the book of Revelation is based on the lament psalms.
4. The early church prayed lament psalms.
Whenham also adds two practical reasons to use lament psalms.
1. Not everyone who comes to church is full of joy and happiness.
2. Praying lament psalms can help one to sympathize with those in trouble and pray for those who are suffering or persecuted.
Gordon Wenham, The Psalter Reclaimed: Praying and Praising with the Psalms (Wheaton, IL: Crossway, 2013), 45-48.