I have no life but this
Double negative logic
"No death, but lest"—she's saying her only death would be *removal* from this state. The grammar is tricky: she fears being "dispelled" the way you'd dispel a ghost.
"Earths to come"
Dickinson uses "earths" (plural) for afterlives or future worlds. She's rejecting both Christian heaven and reincarnation—this relationship is her only reality.
"The realm of you"
Final phrase makes the beloved into a country or kingdom. All her "action" and existence happens inside the territory of this other person.