It's too hard to define "lying" legally. There's too much wiggle room, and truth is a very relative concept anyway, so they will still find ways to get away with saying half-truths as >>14470 said.
Media sources are already heavily reliant on their reputation, nobody will take a news source seriously if it gets out that they lie often (see HuffPo, Daily Mail). Of course the problem is that people have varying opinions on what is truth and what is a lie: Conservatives believe anything supporting liberals is a lie and vice versa. The root cause of this is that the American public is largely uneducated and does not understand the difference between what is not true and what they don't want to be true. In fact, I suspect that if this uneducation was solved (or at least uneducated people were prevented from participating in public discourse) media honesty would take care of itself, since lying outlets could not longer count on being supported by idiots who swallow their lies hook line and sinker because those lies are what they want to hear.
The free market solution is to have a third party organization check and verify news and announce clearly which sources lie and which don't. The problem is that before widespread adoption, much fewer people will follow this rating organization than will follow the news source in question. There is also the question of who runs this organization, how they remain impartial, but that's irrelevant if it will never see widespread use.
The statist solution is to emulate the USSR or the Third Reich. These governments sidestep the problem of defining honesty by instead being very authoritarian and clear about their ideology (unlike modern Western liberal democracies which pretend to have no ideology beyond "being democratic"), it doesn't matter particularly whether you lie or not, but whether you disrupt the government's schemes. This is a much more clear cut distinction, and in these regimes you hardly ever have media which publishes any lies (or facts for that matter) that interfere with government's plans for society. If you happen to be satisfied with the government, great! But where to find a benevolent dictatorship?
The moderate solution is something analogous to the FDA. Have the FCC provide a special "honest" certification to every new company, which can be displayed as a logo in the corner of the TV screen, the website header or the corner of the newspaper page. The right to use this logo is only given after a non-partisan committee of trained journalists and experts within the FCC thoroughly checks your past conduct to verify that you publish factual information only without distorting or misrepresenting the facts. Presumably the public would value honest news more, so this logo will act as a massive pro-honesty incentive for companies.
You still get the same issue as FDA: What if the news corps start bribing the committees, and other such shenanigans? Well, hard to say how you could stop it. But for what it's worth, while there are obviously cases of corrupt dealings between FDA and pharma, I think on the whole the FDA is doing a pretty good job. Any drug you buy will probably list all known information about side effects and the like, all of them are tested in clinical trials, none (barring freak accidents) are spoiled or some chemical other than what the box says, none will outright poison you (unless that's the point, as in chemotherapy drugs). Same goes for food, while companies try to get clever by obfuscating ingredient names and so on, by and large you can look at the ingredients list of a food you buy and get a good idea of what's in it, and thanks to the nutrition values, how healthy (in a very rough sense) it is. I've never heard of a company bribing the FDA so that they can say on the package of their food it contains 30 gr of protein, when it only contains 13. In any case, if FDA was abolished and we had to rely on a private food/drug review aggregator(s), I think the result would be much worse.