You can find a YouTube playlist here with many of the songs suggested below.
Gathering
The Epistle can suggest gathering songs which call for the presence of the Holy Spirit. Come down, O love divine (CH 489 / MP 89) would be a classic opening hymn for this season while Spirit of truth and grace (CH 608) is a great alternative text to the same tune. Other options include Be still for the presence of the Lord (CH 189 / MP 50), Holy Spirit (CCLI), the round Jesus lead us to the Father (Resound) or the short song Come, Holy Spirit, descend on us (CH 589 / MP 818).
For congregations who don’t sing a full setting of the mass every week, one good way to distinguish Lent as a season is to sing a Kyrie as a response to the prayer of confession. This may be unfamiliar liturgically in some traditions but fits the readings well as Psalm 51 sets the tone for the season. CH4 offers three contrasting options which are all easy to pick up with James MacMillan’s Lord, have mercy (CH 648), the Ukranian Orthodox Kyrie eleison (CH 776) and John Bell’s call and response Kyrie eleison (CH 777). This is also a great chance to learn a song from other parts of the world and Khudaayaa, raeham kar (WGRG / PFAS 51G) Ya Tuhanke (WGRG) are from Pakistan and Indonesia, places we rarely sing songs from. Both can be sung in English but try to imitate the slides on the recording of the first which is an important part of the style. Kyrie eleison, have mercy (MP 1321 / Townend) and Kyrie eleison (CCLI) are more suited to worship bands and could be used in full or just a single verse/chorus while Lord have mercy (Resound) would suit a variety of instrumentations. Create in me a clean heart O God (PFAS 51F) isn’t a Kyrie but is also from Psalm 51 and could also be an appropriate response to prayers of confession and Hear the song of our lament (Resound) would be an interesting song to use if you wanted to intentionally bring a whole of creation perspective.
Word
There is a poignancy to the Scottish Paraphrase Lord, from the depths to thee I cried (CH 87) when sung to the tune Martyrdom which really suits the penitential psalm in today’s readings, especially if it is sung a cappella. Out of the depths (Grace) and In deep despair I cry to you (PFAS 130E / link) are metrical versions in more contemporary language set to well known tunes which capture a similar feel. For you, my God, I wait (PFAS 130G) has a lovely lilting original tune but it can also be sung to Southwell, the tune which Out of the direst depths (WGRG) is set to as well. Out of the depths (CCLI / Grace) is a worship song which effectively contrasts verses about times of despair and questioning with a chorus focusing on our hope and trust in God.
Response
Quite a few songwriters have been inspired by the description of Jesus' emotions in the Gospel and particularly v.35. O Christ, you wept when grief was raw (CH 734) is a very accessible option here as it is set to Rockingham while other possibilities include the round When Jesus wept (Hymnary), When Jesus learned his friend had died (GIA) and See how deep (Gordon). You could also consider songs which speak more broadly about the Jesus performing miracles such as God with us (CCLI) and Miracles (CCLI).
Songs which call for the Holy Spirit to transform us would link well to the Epistle including classic hymns such as Breathe on me, breath of God (CH 596 / MP 67), O Breath of life, come sweeping through us (CH 595) and Spirit of the living God (CH 619 / MP 613) as well as more contemporary options such as Holy Spirit, living breath of God (MP 1183 / CCLI / Getty) and Fresh wind (CCLI). Some less familiar songs that are worth considering include Breath of God (Common), As the wind song through the trees (Hope) and the short song Come, come, O Holy Spirit / Ven, Espíritu Santo (GSW 24).
You could use most of the songs suggested for the Epistle for the Old Testament as most of them reference the breath of God and the life it brings. Days of Elijah (MP 1012 / CCLI) has a more explicit reference to this passage in its second verse.
Sending
Themes of new life and renewal could make suitable sending themes for the readings. God, breathe new spirit (GIA) is likely to be new for many but can be sung to Resignation and would link well to either the Gospel or the Old Testament while Earth, earth, awake; your praises sing (CH 420) is generally an Easter hymn but themes of comforting those who mourn and life springing from the tomb could fit well with the Gospel. Some more general but familiar songs that could be suitable include We sing a love that sets all people free (CH 622), The Spirit lives to set us free (MP 664), the wonderful Tanzanian song Gracious Spirit, hear our pleading (CH 613), and worship songs like Fresh wind (CCLI) and Free amen (CCLI).