Last year, I noticed a few small connections between the text and tune of "The Lamb." They all deal with this musical phrase (from the tune "Winter"):
The first and third lines in the hymn are both sung to this phrase.
The third line of the fifth verse is "His song prolong." Both "song" and "prolong" are sung with melismas (F E and E D C, respectively), musically giving a sense of this lengthening.
The first line of the fourth verse is "He sighs, He dies." Here, "sighs" is sung with a melisma (F E), musically giving something of an impression of this action.