What is the best way to address misinformation given in a lecture?
...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.