Meanwhile, the Independent newspaper reported Lennox as saying that O'Connor's video and question of why she did not have close friends or family to help her in the vulnerable state has got her anxious and distressed.
"I'm now living in a Travelodge motel in the arse-end of New Jersey", O'Connor told her Facebook followers. It's like a witch hunt'.
While the Irish singer admitted she was deeply depressed and sometimes had suicidal thoughts, she said she would stay alive for other people in her life. "They said she is not here so I guess I'll just bring the food back".
O'Connor is remembered for her arresting 1990 rendition of Prince's song "Nothing Compares 2 U", and its iconic video featuring the tearful and shaven-headed singer.
Last year, Sinéad reportedly went missing.
She's left the shoddy hotel in New Jersey.
A posting on O'Connor's page post on Tuesday assured fans she was fine.More news: Indian troops kill militant in Indian-controlled Kashmir gunfight
Intense stuff. Nonetheless, the 50-year-old says she hopes her video will be "somehow helpful" to the "millions of millions of millions of people who are just like [her]".
"I'm fighting like all the millions I know to stay alive everyday which I'm doing because I love the people that are doing this to me", O'Connor says. I lost my brother to suicide 6 months ago and it has completely devastated my life.
"I'm awake alone, in labor with the kidney stone still trying to get through the tubes to my bladder", she wrote after the video was shared. "People who suffer from mental illness are the most vulnerable people on Earth", she said. "I don't know who she is".
During the 12-minute long video, O'Connor said she was suicidal and feels like she is being punished for having mental illness. She said mental illness is like addiction in that it doesn't care who you are. "Three f***ing illnesses made me suicidal ..."
She has openly talked about her health issues, saying in 2003 that she was diagnosed with bipolar disorder. The video was posted from a motel in which she says she has been living. "I'm doing my fu***ng best in the world like everybody else". "That's the only thing keeping me alive at this moment".
"I go to bed every night anxious about you. It's a crime and it should not be acceptable to any man that knows me or claims to love me".
O'Connor, known for her shaved head, has been a lightning rod of controversy throughout her career whose antics include ripping up a picture of Pope John Paul II on Saturday Night Live in 1992.