The earliest worship lyrics, as I noted, were straight from the scriptures. Jerub-baal asked in the comments for sources, and I have updated that post, including a link to an online radio station which plays Gregorian chant.
Somewhat more flexibility of lyric began to creep in over the centuries, though the subject matter hewed pretty close to rephrasing biblical sentiments. Notice in "O Come, O Come Emmanuel" (Veni Emanuel) that no single line is quoted from a Bible verse, but every line uses biblical phrases. This is apparent even in this later translation of the 12th Century lyrics.
Veni, veni Emanuel Captivum solve Israel
Qui gemit in exilio Privatus Dei Filio
Gaude, gaude Emanuel nascetur pro te Israel
O Come, O Come Emmanuel And ransom captive Israel
That mourns in lonely exile here Until the Son of God appear
Rejoice! Rejoice! Emmanuel shall come to thee O Israel
O Come Thou wisdom from on high Who orderest all things mightily
To us the path of knowledge show And teach us in her ways to go
O Come Thou rod of Jesse, free Thine own from Satan’s tyranny
From depths of Hell Thy people save And give them victory over the grave
O Come Thou key of David, come And open wide our heavenly home
Make safe the way that leads on high And close the path to misery
O Come Thou root of Jesse’s tree An ensign of thy people be
Before Thee rulers silent fall All peoples on Thy mercy call
O Come, Thou Dayspring come and cheer Our spirit by Thine advent here.
Disperse the gloomy clouds of night And death’s dark shadows put to flight
O Come, O Come great Lord of might Who to Thy tribes on Sinai’s height
In ancient times once gave the law In cloud and majesty and awe
O Come Desire of nations, bind In one the hearts of all mankind
Bid Thou our sad divisions cease And be Thyself our King of Peace
Similarly, in the 16th C "Gaudete" the chorus is not Scripture, but so closely scriptural as to make no difference. The verses, because of the artistic convention of rhyming (in the Latin, not in this translation), get pulled just a bit farther afield. Note: gaudete, "rejoice," is related to our word gaudy. Though the word has the negative connotation now of being overdone, the connection with rejoicing, which suggests exclamation marks rather than mild approval, is clear.
From the Finnish collection of medieval music Piae Cantiones, which I first encountered while listening to Steeleye Span.
Gaudete, gaudete Christus est natus Ex Maria virgine gaudete
Rejoice! Rejoice! Christ is born Of the Virgin Mary, Rejoice!
1. Tempus adest gratiae Hoc quod optabamus
Carmina laetitiae Devote reddamus
1. The time of grace has come For which we have prayed
Let us devoutly sing Songs of joy
2. God is made man While nature wonders
The world is renewed By Christ the King
3. The closed gate of Ezekiel Has been passed through
From where the light has risen Salvation is found
4. Therefore let our assembly sing praises now At this time of purification
Let it bless the Lord Greetings to our King
This technique of the congregation singing or reciting one repeated part while the leader inserts verses between is common in most non-literate cultures. Before slaves were allowed education, the African-American spiritual had this call-and-response form ("Michael Row The Boat Ashore"), and liturgical churches retain this style in the prayers in which the congregation echoes "Lord have mercy." This form makes eminent good sense if you think about it, as it is a very efficient way of allowing everyone to participate while developing greater complexity.
As verses enter the picture, we see the beginnings of story being told in music. Veni Emanuel captures a whole sweep of Old Testament characters and themes. The communal aspect is still very strong: we instead of I, our instead of my still predominate.
Visual break here, because it's important and I want to catch those scanning: The communal words of prayer and song were considered of utmost importance to nearly all earlier ages of the church. One does occasionally find lyrics that use me, my, I, but these were in the specific context of confession, or meditating on Jesus dying for my sin ("O Sacred Head Now Wounded"). As we move into the later ages of the church, we will see that we have lost something when our hymns start to say "He walks with me and He talks with me, and He tells me I am His own." It's a nice sentiment, but something precious has been lost.
A related type of lyric is the doxology (glory + word), a form which predates the Christian era but was popular in the medieval church. The Tallis Canon, the Gloria Patri, and "Praise God from whom all blessings flow" are among the oldest pieces still commonly sung in English in our churches.
Other early lyrics we still keep: "All Creatures of Our God and King," "All Glory, Laud, and Honor," and "Let All Mortal Flesh Keep Silent."
The only real rivals to these pieces for age are some Christmas carols, which we also tend to hang onto fiercely. The carols, sometimes based on folk tunes for pagan festivals, were not always accepted in formal worship. One can still see the conflict of Christian interpretation being imposed on non-Christian elements in such carols as "The Holly and The Ivy," "O Tannenbaum," "The Boar's Head Carol," and the various Wassails.
The First Nowell c. 1600 AD
I saw 3 ships 1500
Good King Wenceslas 1500
A Babe is Born 1350
The Angel Gabriel 1450
In Dulci Jubilo 1350
Lo How a Rose Ere Blooming 1600