Answer:
When Emily Dickinson laments that her life has closed twice before its close she is telling the reader that her parents have both preceded her in death. Dickinson lived life as a recluse. She was particularly close to her father (as many daughters are) and after his untimely death, she and her fellow spinster sister had to care for their mother who becamebedridden and incapacitated a year later. Her mother remained that way for nearly ten years. Still Dickinson's life revolved around around them since besides poetry and gardening, she had little else going on in her life. Once you realize this about the first line, the rest of the poem makes sense.