In context with the entire piece, Byron's "When We Two Parted" seems to reflect the speaker's sense of loss over a departed lover. While the poem begins by referring to their separation, the third stanza seems to address more than the end of their relationship, but her physical death.
While there are words throughout the poem that speak of a loss to the grave (such as "grieve" and perhaps "spirit"), in this stanza one that could be taken figuratively, but speaks literally to me—of her passing: knell. Knell can be defined literally as:
...the sound made by a bell rung slowly, especially for a death or a funeral.
It can also be defined figuratively:
...a sound or sign announcing the death of a person or the end, extinction, failure, etc., of something...
Historically, when someone of importance died, bells in a church tower would toll announcing that death. Similarly, when a casket was passing through a town to its resting place, someone would ring a bell to announce its passing, but also the "passing on" of the spirit of the individual inside. (This is mentioned in Chaucer's The Canterbury Tales, in "The Pardoner's Tale.")
Another word, "shudder," brings to mind a physical reaction—perhaps to death:
The stanza begins with "they" (which could be people telling him news or words at a funeral service by the clergy) and states...
They name thee before me...
It is certain that discussion is taking place, but we must ask in what context is the name mentioned? Hearing her name is like a death sound to him, like...
...A knell to mine ear...
And when he hears the name, he trembles:
A shudder comes o'er me...
He wonders what about her touched him so deeply.
Why wert thou so dear?
The next two lines tell us that their relationship was a secret, for "they" (the speakers) are unaware not only that he knew her, but that he "knew thee too well." This could refer to the depth of their relationship—that it was a clandestine love or a forbidden love, and also that (in light of the final stanza) he might be knowledgeable (because of their relationship) that she was not as pure in life as others might have thought her to be ("Thy spirit deceive...") in having this love affair. It would have been deemed sinful to have a relationship with a man without being married to him, or to have had an affair with a married man. We aren't certain why the relationship was a secret to begin with.
If the speaker had said "Long shall I rue thee," I could imagine he is stating that he will have "bitter regret" or "sorrow" ("rue") for years to come. However, the use of the second "long" makes me feel that this regret will remain now for the rest of his life. She is gone and in this situation, he will now never be able to work things out with her, or find peace regarding their separation: it can never be addressed between them now.
The last line of the stanza simply conveys the speaker's inability to put into words how much sorrow he feels—potentially still for the end of their love—but perhaps now for her passing.
This eight-line stanza follows an ABABACAC rhyme scheme. There are generally two stressed syllables per line (scansion). (The second "long" in line #7 could simply maintain this rhythm, but there is no way to know the purpose of its placement for certain.)