The Navy lied to everyone about what happened, and not a 'small' lie either.
I think you're reading a bit more malice into the Navy's decision then was present.
In practice, this
was a small lie, the revealed information doesn't change anything significant in terms of capabilities or hardware, the Navy wasn't trying to conceal its own ineptitude or role in the disaster as it has for other incidents.
It seems more likely they lied to comfort the crew’s families, opting to tell them a version of events that implied thier loved ones died quickly. I can't really blame them for that.
You could argue it was done to make sure the incident wouldn't make it harder to recruit more submariners, however it was already well known that being on a sub meant you might slowly die in a big metal tube, trapped deep underwater with no way out (this is one of the reasons why sub crews have always been volunteer only). That's been a risk submariners knowingly take ever since the Hunley (or at least the Hunley's second crew. Maybe the first one didn't quite know what they were in for).
Any hopes for lawsuits from crew family members?
Almost certainly not. It's hard to sue the government under normal circumstances, sueing the military because of an equipment malfunction or poor design choice, that's not going to happen, because sometimes that's just how it is.
Edit: To clarify, consumers are generally entitled to fairly strong protection in terms of product design and safety standards, and it's viewed as being inexcusable to expose consumers or employees to severe danger.
The military, however, operates under different standards. It carries out missions that are innately dangerous and that have stakes that are far more important than any single persons life, and consumer standards don't and can't apply.
In the civilian world, demanding your employees use equipment that is not rated for the task at hand will land you in jail. In the military, if there's a flight of incoming Zeroes and all you have are some F4 Wildcat, then you launch the wildcats and engage, no matter how outmatched the wildcats are.