In the poem "A Nocturnal upon St. Lucy's Day" by John Donne, the narrator is mourning his lover, who has died. The world has become a dark and dismal place for him, because he found love and then lost it.
St. Lucy's Day is celebrated in certain European countries in honor of Lucia of Syracuse, who risked her life to bring food to Christians who were hiding out in the catacombs beneath the city of Rome. However, the significance of St. Lucy's Day to this poem is that in Donne's era (though no longer), the celebration took place on the Winter Solstice, which is the shortest day of the year. On this day, there are only a few hours of daylight, probably around "seven hours" in England, as Donne specifies in the poem, followed by many hours of darkness.
The poet uses St. Lucy's Day as a metaphor of the narrator's situation. He enjoyed a short time of light and joy while his lover was present with him, and now he endures a long period of darkness, which has reduced him to nothing.
Due to the inner darkness he is experiencing, at the end of the poem, the narrator expresses his observation that the "long night's festival" of St. Lucy's Day is a fitting time for him to hold a vigil for his lost love, since the day has been plunged into "deep midnight."
To understand the reference to Love's limbec, we must understand the meaning of the word. A limbec (spelled "limbec" in the Free Dictionary but spelled "limbeck" in the Merriam-Webster Dictionary) is defined as an alembic, which is "an apparatus used in distillation; or, something that refines or transmutes as if by distillation." In the context of the poem, the second definition applies. According to the narrator, his "life, soul, form, spirit" have been distilled or reduced to nothing by Love's limbec—that is, by the tragedy of losing his loved one.