The family alleges that their son's interaction with ChatGPT and his eventual death "was a predictable result of deliberate design choices".
They accuse OpenAI of designing the AI programme "to foster psychological dependency in users," and of bypassing safety testing protocols to release GPT-4o, the version of ChatGPT used by their son.
The lawsuit lists OpenAI co-founder and CEO Sam Altman as a defendant, as well as unnamed employees, managers and engineers who worked on ChatGPT.
In its public note shared on Tuesday, OpenAI said the company's goal is to be "genuinely helpful" to users rather than "hold people's attention".
It added that its models have been trained to steer people who express thoughts of self-harm towards help.
The Raines lawsuit is not the first time concerns have been raised about AI and mental health.
In an essay published last week in the New York Times, writer Laura Reiley outlined how her daughter, Sophie, confided in ChatGPT before taking her own life.
Ms Reiley said the programme's "agreeability" in its conversations with users helped her daughter mask a severe mental health crisis from her family and loved ones.
"AI catered to Sophie's impulse to hide the worst, to pretend she was doing better than she was, to shield everyone from her full agony," Ms Reiley wrote. She called on AI companies to find ways to better connect users with the right resources.
In response to the essay, a spokeswoman for OpenAI said it was developing automated tools to more effectively detect and respond to users experiencing mental or emotional distress.
If you are suffering distress or despair and need support, you could speak to a health professional, or an organisation that offers support. Details of help available in many countries can be found at Befrienders Worldwide: www.befrienders.org.
In the UK, a list of organisations that can help is available at bbc.co.uk/actionline. Readers in the US and Canada can call the 988 suicide helpline or visit its website.