Lord Byron was well known for his many and frequent love affairs. "When We Two Parted" was most likely written for Lady Frances Webster, with whom Byron had an affair. He did not include her name or specific details in the poem, because she just happened to be the "unhappily married wife of a close friend" ("Lord Byron's lovers"). Despite his efforts to keep a lid on his affairs, many of Byron's escapades became well known, especially that of his most public affair with Lady Caroline Lamb. Even after he tried to break things off with her, she pursued him and made several public scenes. After the debacle of that relationship ended, Byron endeavored to be more discreet in his relationship with Lady Frances to protect her identity and reputation.
Research has revealed an unpublished section of the poem in letters to Byron's cousin, Lady Hardy, which discloses the identity of the mystery lover as Lady Frances:
". . I [Lord Byron] send you the concluding stanza --- which never was printed with the others. ---
Then --- fare thee well --- Fanny ---
Now doubly undone ---
To prove false unto many ---
As faithless to One ---
Thou art past all recalling
Even would I recall ---
For the woman once falling
Forever must fall. ---" (qtd in. Byron's Letters and Journals).
The mention of "Fanny" in the missing stanza is, of course, Lady Frances.
Byron, Lord George Gordon. Byron's Letters and Journals Vol. X. Ed. Leslie A. Marchand. Cambridge: Belknap Press, 1980. print.
"Lord Byron's Lovers." English history. web. 24 Jul. 2012.