2:03 PM PT -- John Barnett's family released a statement on their loved one's passing, and they reiterated his cause of shining a light on safety concerns that he was raising while at Boeing -- noting he was deeply affected by the lawsuit he was embroiled in, which they say was going to trial in June. His family says they believe his experience at Boeing contributed to his death.

The Boeing whistleblower's attorneys say he didn't appear suicidal before he died -- which is why they think his death is incredibly suspicious ... and are calling for answers immediately.

Robert Turkewitz and Brian Knowles -- who were repping John Barnett in a retaliation lawsuit against Boeing, which was well underway -- tell TMZ ... Barnett was in the middle of depositions last week in his civil case, a process they say was nearing an end soon.

We're told Barnett was in good spirits and very much so looking forward to putting this whole saga behind him, ready to move on. They add, "We didn't see any indication he would take his own life. No one can believe it."

They add, "We are all devastated. We need more information about what happened to John. The Charleston police need to investigate this fully and accurately and tell the public what they find out. No detail can be left unturned."

The attorneys explain that Barnett had filed suit because he felt Boeing had retaliated against him after he tried sounding the alarm on what he believed was them turning a blind eye to safety issues ... and alleged in his lawsuit they'd fostered a hostile work environment.

Like we said ... Barnett's case seemed to be wrapping up -- and amid reports Barnett took his own life in the middle of all this, it's safe to say his legal team is incredulous. Knowles was even quoted as calling the self-inflicted wound being attributed to his client "alleged."

As we reported ... Barnett had been going around and speaking very publicly about the issues Boeing had been experiencing lately -- even coming onto our own show, "TMZ Live."

He explained why he felt them getting the green light to hit the skies again so soon after the Alaska Airlines incident was dubious -- claiming this was in line with his own experience with Boeing as a quality manager ... a period during which he alleged he saw many lapses.

In the aftermath of our chat with Barnett, Boeing planes have continued to experience problems -- including something dramatic just this week ... with a flight from Australia to New Zealand beginning to drop out of the sky after apparent massive equipment failure.