It's almost always a safe bet that a Donne poem will be about a woman, God, or death—or some combination. So, even though this is a love poem, it's not too surprising that we start off with a metaphor about an old man dying. In this poem, though, Donne gives death dignity—it's a peaceful and welcome thing. It's also his first connection to love. Even though their parting will feel a little like a death, their love is so pure, powerful, and good that they can endure it gently, without any outward sorrow.
Line 1: The key condition (according to Donne) for a peaceful death was a "virtuous" life. Because they didn't have any regrets or guilt weighing them down, these righteous people are able to slip into death like a warm tub—morbid, but nice.
Line 2: Donne was so fascinated by death because (as his theology held) that was the point at which the body and soul parted ways. In this case, the dying man is able to whisper his soul out of his mortal body and on to heaven.