If the Exeter Book had not survived, there would be no Wife's Lament. The manuscript, known to palaeographers as Exeter, Cathedral Library 3501, contains the only copy of the poem we have.
The poem in its most immediate context
The Wife's Lament occupies both sides of folio 115 of the Exeter Book. It is important to consider how the poem fits into the overall arrangement of the vernacular poetry in the manuscript. The Exeter Book opens with long poems: a series of poems chronicling Christ's birth, death and second coming (Advent, Ascension and Christ III), a pair of poems celebrating the deeds of St Guthlac (Guthlac A and Guthlac B) and three thematically-connected religious poems (Azarias, Phoenix and Juliana). Here the principle of arrangement becomes less clear. Certainly, the poems that follow are shorter. Altogether, they are best described as 'wisdom literature'. Within this group of wisdom poems are 'elegaic' poems like The Wanderer and The Seafarer, formal experiments like The Riming Poem, bestiary poems, two sets of riddles and short homiletic poems.
The Wife's Lament is the first poem in a sequence of miscellaneous short poems which sit between the two series of riddles. Sisam (1953) suggested these poems (Wife's Lament, Judgement Day I, Resignation, Descent into Hell, Alms-Giving, Pharaoh, Lord's Prayer I, Homiletic Fragment II, Riddle 30b, Riddle 60, Husband's Message, and The Ruin) formed 'a patch of collected material that was not digested into the original plan'. You'll have to think whether Sisam is right.
The poem in its scribal context
The scribe who wrote all of the Exeter Book also wrote two Latin manuscripts: a copy of Bede on the Apocalypse and Augustine on adulterous marriage (London, Lambeth Palace Library, 149) and a copy of Isidore on the Catholic faith (Oxford, Bodleian Library, Bodley 319). He was probably writing between during the 960s and 970s. Where he was writing is even less certain. It is unlikely to have been Exeter itself. Other suggestions are little more than educated guesses.
The poem in its geographical context
Though the origin of the Exeter Book is uncertain, we can be reasonably sure that it was given to his see by Leofric, bishop of Exeter, between 1050 and 1072, by when an inventory of his gifts to the cathedral had been drawn up. Exeter, having been sacked by the Vikings in 1003, barely survived until 1050 when Leofric made it the centre of the bishopric of Devon and Cornwall. An adulatory note in the Leofric Missal records that all that remained of Exeter's endowment on Leofric's arrival was one very poor piece of land (this out of the twenty six given by King Æthelstan), three books and a chest of relics (feretrum reliquarum). Leofric therefore set out to enrich Exeter fittingly. He restored lands that had unlawfully been taken from the cathedral, acquired new lands, bestowed precious ornaments for the altar and gave books. All these gifts are listed in the famous inventory (edited by Lapidge (1994), X). The inventory was written into two gospelbooks to ensure his generosity would be forgotten neither by man nor by God.
Leofric gave the books essential for the divine office (gospelbooks, missals, epistolaries, antiphoners, psalters, hymnals, a collectar, a gradual, a benedictional and so on) and a set of the most important Latin biblical commentaries and reference works. Two items stand out: a copy of the Old English translation of Boethius, De consolatione philosophiae and 'a large book in English about various things written in verse' (i mycel englisc boc be gehwilcum þingum on leoðwisan geworht). This latter item has been identified as the Exeter Book. Where Leofric acquired the Exeter Book is not clear, though the other entries on the list make clear his abilities at sourcing second-hand books, whether legitimately or no. The question to ask is this: why would Leofric have felt a manuscript containing the poem The Wife's Lament was a suitable gift for this community of secular canons in the third quarter of the eleventh century? Few critics have tried, none have succeeded.