"It's terrible to see her in such a vulnerable state."
Lennox is one of many to rally around the troubled Nothing Compares 2 U singer after she posted the the clip on Facebook last week.
O'Connor revealed in the video that she was all by herself at the $70-a-night Travelodge motel in the 'a**e end of New Jersey' and fighting to stay alive every day.
In the video filmed from the bed of her room in Hackensack, the mother-of-four said: "I am now living in a Travelodge motel in the a**e end of New Jersey. I'm all by myself.
"And there's absolutely nobody in my life except my doctor, my psychiatrist - the sweetest man on earth, who says I'm his hero - and that's about the only f***ing thing keeping me alive at the moment...and that's kind of pathetic.
"I want everyone to know what it's like, that's why I'm making this video.
"Mental illness, it's like drugs, it doesn't give a s*** who you are, and equally what's worse, it's the stigma, it doesn't give a s*** who you are.
"Suddenly all the people who are supposed to be loving you and taking care of you are treating you like s***. It's like a witch hunt."
The troubled Irish singer-songwriter said she was "fighting like all the millions of people" battling a mental illness.
"If it was just for me I'd be gone. Straight away back to my mum... because I've walked this earth alone for two years now as punishment for being mentally f***ing ill and getting angry that no one would f***ing take care of me," she said.
"I'm a 5ft 4in little f***ing woman wandering the world for two years by myself."
She also added that she had been in hospital for kidney stones recently.
A post on O'Connor's Facebook page on Monday read: "Hi everybody, I am posting at Sinead's request, to let everyone who loves her know she is safe, and she is not suicidal."
"She is surrounded by love and receiving the best of care. She asked for this to be posted knowing you are concerned for her. I won't respond to any questions, so please understand. I hope this comforts those of you were concerned."
A woman staying at the motel told Page Six that O'Connor had been staying there for a week. "She had a hospital band on her wrist," the woman said.
The woman added that O'Connor kept to herself but "left her door wide open all week except at night" and would often go to the Pepsi machine.
O'Connor has spoken previously about how she was diagnosed with bipolar disorder more than a decade ago and has struggled with depression and post traumatic stress for years.
She told Oprah Winfrey in 2007 that before her bipolar diagnosis she had struggled with thoughts of suicide and overwhelming fear.
She said at the time that medication had helped her find more balance, but "it's a work in progress".
O'Connor said in later interviews that she was misdiagnosed with bipolar disorder in 2011.
The mother-of-four sparked a police search in May last year when she failed to return from a bike ride in suburban Chicago.
About two hours after she left on the ride, a rambling message was posted on her official Facebook page that referred to emotional trauma she had been through over the years, prompting fears she had disappeared to take her own life.
She was found by police later that day at an unidentified hotel.
O'Connor, who is a mother to four children from different relationships, took to Facebook in 2015 to say she had taken an overdose at a hotel somewhere in Ireland.
Irish police later said she had been found safe. The next month, she posted on Facebook that she had been detained in a hospital for mental health evaluation.
Comedian Arsenio Hall dropped a $5million lawsuit against O'Connor earlier this year after she apologised and retracted comments she made on Facebook that he had supplied drugs to Prince.
WHERE TO GET HELP:
If you are worried about your or someone else's mental health, the best place to get help is your GP or local mental health provider. However, if you or someone else is in danger or endangering others, call 111.
If you need to talk to someone, the following free helplines operate 24/7:
DEPRESSION HELPLINE: 0800 111 757
LIFELINE: 0800 543 354
NEED TO TALK? Call or text 1737
SAMARITANS: 0800 726 666
YOUTHLINE: 0800 376 633 or text 234
There are lots of places to get support. For others, click here.
