You can find a YouTube playlist here with many of the songs suggested below.
The psalm is a great gathering text as it calls us to sing to God with joy and there are a huge range of songs you could use for this including classic hymns such as Let all the world in every corner sing (CH 122) and Rejoice! the Lord is King (CH 449 / MP 575), worship songs such as Let everything that has breath (MP 1001 / CCLI), My Jesus, my Saviour / Shout to the Lord (CH 531 / MP 1003 / CCLI) and From life’s beginning (Let praise resound) (Resound) or songs from around the world such as Uyai mose / Come all you people (CH 757), Cantai ao Senhor / Let’s sing to the Lord (CH 126) and Mari beribadah / Let us come and worship our Creator (H 37).
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.
Oh, come, and let us to the Lord (CH 59) is a classic metrical setting of the psalm with two options for tunes, of which Irish is probably the more familiar but Bon Accord gives a wonderful lift to the singing when sung strongly in parts. Come, let us praise the Lord (CH 60 / PFAS 95A) is an option for those who prefer contemporary language and can be sung either to the Chilean Venite or to Darwall’s 148th. Let us shout for joy (link) and Come let’s sing (Resound) would both be great for bands and really capture the joyful spirit of the psalm. Let’s sing unto the Lord (CH 176) from Mexico and Come now, and lift up your hearts (STB 91 / PFAS 95F) from South India are both very strong stylistically but easy to pick up while Venite, exultemus Domino (Taizé) could be used either as a repetitive chant or for singing the psalm responsorially.
There are songs which link directly to the Gospel story such as Like the woman at the well / Fill my cup, Lord (Hymnary / link), A traveller unknown to me (GIA) and As Jesus journeyed with his friends (Carolyn) sung to Tallis’s Canon. However, there are many better known songs which have a wider focus on the living waters such as I heard the voice of Jesus say (CH 540 / MP 275), Praise the One who breaks the darkness (CH 348), Spirit of God, come dwell within me (CH 722), Come to the feast (GIA), All who are thirsty (MP 1025 / CCLI) and Living waters (CCLI / Getty).
There is a strong link between the Old Testament and Gospel passages today and so some of the hymns suggested above could also work for the passage from Exodus. There are also some classic hymns which would link strongly such as Guide me, O thou great Jehovah (CH 167 / MP 201) and Glorious things of thee are spoken (CH 738 / MP 173) while As the deer runs to the river (Hymnary) is a more contemporary one to consider.
The Epistle covers a lot of ground and it’s a challenge to find songs which capture all of it. Some songs which could link in different ways include By faith (MP 1262 / CCLI / Getty), We sing the praise of him who died (CH 405 / MP 738) and My hope is built on nothing less (MP 473 / Hymnary) or the two great reworkings of it - the Kenyan song Kwake yesu nasimama (GSW 34 / GIA) and the popular worship song Cornerstone (MP 1334 / CCLI). Holy Spirit, fill our hearts (CH 611) and Come, Holy Spirit gracious heavenly dove (CH 758) would specifically link to v5 and God’s love being poured into our hearts through the Holy Spirit.
Some of the songs suggested above would excellent final songs if you haven’t used them already, such as Guide me, O thou great Jehovah (CH 167 / MP 201), Glorious things of thee are spoken (CH 738 / MP 173) and Cornerstone (MP 1334 / CCLI). You could also use songs which link to the living waters such as Jesus, lover of my soul (CH 490 / MP 372), All my fountains (CCLI), Come thou fount of every blessing (Hymnary) or alternative versions of this like Come thou fount (I will sing) (CCLI) and Come thou fount (above all else) (CCLI).