This is generally regarded as a Lenten hymn, but 1) things feel a little Lenten around here right now, and 2) the last two stanzas (which are almost never included by hymnal editors) take a little of the Lenten-ness out of the hymn.
I’ve given the text here as amended by Nathaniel Micklem (1853-1954). He only altered parts of stanzas 1 and 3, and Erik Routley gives the reasons for this in his A Panorama of Christian Hymnody (excerpt below). I’ve put the hymn to the tune ESSLINGEN, with which this text is paired in the Hymnal of the Moravian Church. I find it a much more appropriate tune than the early American melody CLEANSING FOUNTAIN (the unhappy marriage of this text to that bouncy tune is also discussed in the Routley excerpt below). The following text emendations and tune pairing have resurrected this hymn for me: perhaps as I have, you will find in this text and tune a new, old treasure that you can use with your church.
Here’s what Routley had to say:
[This text] is the most difficult case in all hymnodic criticism. In its original version, with the opening, “There is a fountain filled with blood drawn from Immanuel’s veins,” it has secured the affection of many devoted disciples and earned the execration of as many people who find it crudely revolting . . . The passage behind this opening stanza is this, in the King James Version of Zechariah 13:1:
In that day there shall be a fountain opened to the house of David and the inhabitants of Jerusalem for sin and for uncleanness.
Cowper’s intention is to identify this, through an accepted course of typology, with the blood of Christ shed on the Cross. Were it not that a later English poet whose gifts I should not place much below Cowpers (i.e., Micklem–JATB) has produced an amendment that reflects the original Scripture more faithfully (in the words “for sin”) and that introduces the majesty and pathos of the Atonement with no less sureness and without the graceless literalism into which the usually sensitive Cowper was betrayed, I could not pursue this argument . . .
But my reasons go beyond this. For one thing, this amendment is at present (i.e., in 1979–JATB) wholly unknown to editors, and therefore nowadays the hymn appears only in those collections which do not make much allowance for the antipathetic reaction I have mentioned; for another, when the hymn is printed it often ends at stanza 5, or, much worse, is further abridged and presented with a spurious chorus, and, to crown it all, a shockingly complacent and jaunty tune (CLEANSING FOUNTAIN), so that contemporary associations with it are further corrupted. (Erik Routley, A Panorama of Christian Hymnody, p. 38.)