This claim is unverified because the provided reporting documents serious concerns about conditions and mental health aboard the USS Abraham Lincoln but does not substantiate that sailors were required to sign nondisclosure agreements before leaving the ship.
Navy Sailors being made to sign NDA’s before leaving the Abraham Lincoln.

US navy veterans and military health experts express concern over USS Abraham Lincoln sailors - US military | The Guardian
Source: theguardian.com
Key Evidence
The Guardian, BBC, TIME, CBS News, CNN, ABC News, NewsNation, and The Independent all describe concerns involving the Lincoln's prolonged deployment and sailors' welfare.
The supplied excerpts do not mention nondisclosure agreements or mandatory signatures before departure.
The strongest available conclusion is therefore that the underlying conditions are being widely reported, while the specific NDA claim remains unsupported by the provided sources.
What the Evidence Shows
The available sources consistently focus on the carrier's extended deployment, alleged food and plumbing problems, deteriorating morale, mental health concerns, and reports that sailors considered or went overboard. Several articles also describe congressional inquiries and disputes between military families and Navy leadership.
However, none of the provided search-result excerpts reports that sailors were required to sign NDAs, identifies an official order imposing such a requirement, or provides documentary evidence such as an NDA form, Navy directive, legal notice, or firsthand account specifically confirming the allegation.
The claim may be circulating in connection with reports about sailors' communications, departure procedures, or Navy efforts to manage information during the deployment. Those possibilities cannot be established from the supplied evidence. The reporting about difficult conditions should not be treated as confirmation of the separate NDA allegation.