The main idea behind the poem is that one should calmly accept the inevitable death that awaits us all. To that end, the speaker urges her beloved not to grieve over her death in the conventional manner when the time comes. There must be no planting of roses at her grave and no singing of sad, mournful songs. Instead, the speaker's lover should "Be the green grass above me", i.e., he should move on with his life. Whether he remembers his dear departed or forgets about her altogether, it doesn't really matter. Either way, she'll still be dead.
The second stanza is deliberately ambiguous, reflecting the inability of any one of us to talk meaningfully about what happens to us when we die. The speaker can tell us what it won't be like when she passes away, but not what it will be like. After she's departed and her soul finally reposes in the twilight of eternity, either she will remember her life on earth or she will have forgotten about it altogether, just as the speaker's beloved will either remember or forget all about her when she's gone, as we've already seen. In both cases, it doesn't much matter, because in the final analysis, the speaker will still be dead.