What is the best way to address misinformation given in a lecture? After having reviewed a similar question while looking for an answer to my own, I felt it did not get fully at the heart of my issue that I've come across. However I still feel that it has great relevance to my own query. 

The original post now a bit over 3 years old "How should students react to inaccuracies in professors' teaching without causing resentment"

My question: 

What is the best manner to approach a professor about false information given during a lecture? However, this was not merely a miss recalled information or a slip of the tongue. Rather it was a focal topic for a little over an hour out of the two and a half hour lecture time. Based on a premise that has been proven to be objectively false. However It's not as if their claim has only recently been proven false, or that it was only proven false by some singular and obscure study, or that this is information you'd have to really look hard for in order to find. Instead it has been known to be false for the past 6 to 10+ years. On top of that: there has been a virtual hail storm of peer reviewed publications and criticism contributing their own findings that further disprove what my professor claims to be fact. I'm not going to suggest willful misleading for the sake of some tinfoil hat agenda, but the level of negligence on the topic from the professor here was astounding.

To make matters worse the topic is quite sensitive and the professor has made note on how uncomfortable they are when lecturing on the topic because of how sensitive it is. I fear this may lead to some clam shelling if I approach about it. I also am concerned about what kind of world view shaping is occurring because of this false information being touted as fact if left unchallenged. 

I have the opportunity to present oral presentations on works of my choosing - which just so happen to cover the breadth of material that unequivocally refutes the false information given during the lecture. My gut says this is the wrong way to do this. However I am confident that the professor would be less than open to addressing the class with something like:"hey folks the thing I talked about at length yesterday was a based on a premise that has been proven to be false for quite some time now. So forget everything I said about that because it was all based on mis/inaccurate information"

I can empathize immensely with the 3 year old poster and their peers suggestion of "picking my battles" might be the best way to go here.... However I can't help but I feel like I need to say something about this. To let fellow attendees know that the information presented to them was actually false.
...the topic is quite sensitive and the professor has made note on how uncomfortable they are when lecturing on the topic

I am confident that the professor would be less than open to addressing the class...

My gut says this is the wrong way to do this...

Okay, so you've sold me on "let's try something else", rather than publicly calling this person out.

If they are not likely to change their mind, then I assume you want to do something about it in the spirit of being "true to your subject", not wanting false information disseminated by an academic. However, your comment suggests that they may not have actually done "any research on it", which is problematic.

Given all of this, I recommend going to the professor privately and explaining the research you've done. Let him/her come to the realization based on your evidence, if indeed he/she hasn't read the same information you've read. If they seem unwilling, I would suggest bringing this up to the class.

Coming from a (perhaps?) less argument-prone subject, where nearly every claim is testable or provable, I can only sympathize with what must be a difficult choice for you to make. That said, now a question:  If you have ever taught students of your own, how would you deal with a student who, say, rejects a commonly-held claim because they find fault with something in the research (e.g. methods, sample size, confounding variables not accounted for, etc.). How would you handle a conversation with such a person? This might be a way to determine how you might deal with this professor.

Now, obviously it could depend on the forum (an in-class comment, a question in private, etc.), but you might want to correct this person's confidence in the research, and you might want to protect other students from adopting such skepticism. With your professor, however, this will be a harder nut to crack, it seems. Without trying to put them in their place yourself, I suggest letting the facts speak for themselves. Let her/him know what you've found. If this professor seems unwilling to yield to the evidence, then you may just have to accept the fact that people assert all kinds of things all the time, whether true or false. If there are negative repercussions in store for you, you'll have to decide if playing this part is worth it for you.