Topical example (concerning the Facebook bias controversy of May 2016): if Facebook knowingly discriminated against conservative stories in its Trending feature, but told users and the press that there was no bias, could Facebook be prosecuted under U.S. law?
No. In the United States, lying is not a crime.
Unless it is done:
- under oath (in which case it's called perjury) or
- to a law enforcement agent conducting an investigation (in which case it's called obstruction).
There are also the civil torts of slander (oral) and libel (written) if someone lies and damages the reputation or business interests of a person or company. Collectively, and without distinction, these are called defamation.
Lying also has a close cousin — the civil tort of fraud — which usually applies to inducement into a transaction or a contract.
There are also consumer protection statutes (federal and state) that deal with truth in advertising, truth in lending, lemon laws, etc. But those are primarily civil statutes and the last two are pretty far afield from your question.
But none of that applies to the Facebook case you described. So, no.
As @Mowser said in the US, no.
However, if this information was delivered to their customers in, say, Australia, they could be prosecuted there.
It is illegal for a business to engage in conduct that misleads or deceives or is likely to mislead or deceive consumers or other businesses. This law applies even if you did not intend to mislead or deceive anyone or no one has suffered any loss or damage as a result of your conduct.
The law specifically applies to information providers.
Penalties for large corporations typically run into the millions of dollars.