Irony occurs when there is a gap between what we expect to happen and what actually occurs or when words work out to mean the opposite of what they are meant to mean.

The irony in "Her Immorality" is subtle for a modern audience, as we live in a secular age. The twist in the poem—and what makes it modern—is that the speaker would love to join his beloved by dying, but he can't. She pleads with him from beyond the grave to stay alive, because everyone else—all her family and friends—have forgotten her. Should he die, nobody else would remember her and she would have no trace of herself left on earth. She says to him,

In you resides my single power
Of sweet continuance here....

This is ironic for the Victorian era, because it overturns the assumption that one lives on in the afterlife—that God brings immortality. Moreover, it overturns the sentimental assumptions of the Victorian age that the dead are ever cherished by their families. In this case, the family is indifferent to the dead woman and has forgotten her. It's hard to overstate how shocking—so opposite to expectation—this idea would be for a nineteenth-century audience to read in a poem, though it was no doubt sometimes true in real life.

Another layer of irony exists in the fate of the beloved. He is unhappy without his beloved and wants to join her, but he now bears the added burden of fearing death because it means the end of anyone remembering her at all. To stay alive is grief, but, ironically, to die is also grief:

But grows my grief. When I surcease,
Through whom alone lives she,
Ceases my Love, her words, her ways,
Never again to be!