I studied history and I've been working with sources for more than 10 years now. I don't publish (I'm not an academic) but I do collaborate with some projects, mostly Medieval atlases, map-making efforts and the like. I don't have specific sources for this, since it comes from my own experience, but here comes nothing.

Sources lie, all the time. But are you referring to historical sources being manipulated, or modern historians manipulating sources?

In all these years I've grown to both appreciate and despise historical sources, because 1) They are usually terribly biased, and 2) They also give us insight into the mind and intent of the writer.

I've also learned that, even if they're much more tedious to research, notarial and bureaucratic sources are always more reliable. Baptismal and marriage documents, purchase contracts, last wills, etc.

But when it comes to the "histories" (the chronicles, the annals, the hagiographies, the panegyricals...), one should always, always be wary of the content, and only when you've read all that an author wrote, only then do you have an overview of that author's approach, intentions, obsessions, pet peeves and biases.

Take the reign of Caligula, for example. Most of our sources are Suetonius and Cassius Dio, both writing between half a century and a century after Caligula's death, and both with very specific intentions: to slander. Suetonius' text is a very obvious sensationalist collection of morbid trivia, not even given in chronological order, while Dio's account is more thorough, but reading the rest of his work reveals a strong pro-Senatorial streak, which makes him, invariably, assign similar bad traits to "bad emperors" (i-e- those who acted against the privileges, wealth or life of senators) and "good emperors" (those who sought senatorial collaboration in their rule). So, with two sources which seem very biased to begin with, we can't really be sure about stuff as basic as "was Caligula really mad?". Roldán Blázquez argues in his manual "History of Rome" vol II, that Caligula may have attempted (and failed) to create a Hellenistic-style autocracy in Rome, complete with divine royalty, which was opposed by the senatorial aristocracy, which would have allowed senatorial writers to define what was and was not acceptable in a Roman emperor going forwards through their portrayal of the "bad emperors" as dissolute, incestuous, narcissistic, petty and cruel. The problem is, this is impossible to prove. It may seem more likely, but mad Caligula is also equally plausible following the sources we have, which do seem to indicate that Caligula had grand plans, but usually paint them in a bad light.

The example of Caligula is just one of many. Take the lifes of the Visigothic kings of Spain or the first Merovingian kings of the Franks. We have next to nothing to go on. Some hagiographies that usually re-tell Biblical stories, severely biased chronicles written by relevant churchmen with very specific goals in mind, and a handful of letters. One could choose to read the chronicles and believe them to the letter, but that would be the same as attempting to chronicle the 2010-2020's by watching only Breitbart (an example of an outlet which chooses to focus their delivery of information on two or three very specific messages, and will therefore often omit stories which don't fit the messages or don't allow for a reading of those messages in them).

If you want to have access to up-to-date and generally (academically) neutral historical accounts, I recommend academic manuals. Divulgative history is often simplified, school textbooks often push political agenda (of whatever colour) and while historians can disagree (and they do, oh my they DO) they often will refer to sources as the source of their disagreement, which allows you to judge for yourself if you have access to the sources.

TL:DR is that yes, sources are messy, and one needs to be an expert on the moment and the author to be able to be really critical of them. Since no one can be an expert on everything, not even every historical time period, not even about everythin in one specific period... one must rely on historians doing their job well. So, while sources lie all the time, historians generally try to be conscious about how they may be biased, and that makes them more truthful, at least in intent.