How should I handle a situation where the owner of a company is lying to my coworkers? An example scenario would be "The company took a loss last year". The reality is that the private company actually recorded a profit and both the owner and I know that.
As commented, you could stand up and shout in front of everyone that the owner is lying, but I think we all know that's not going to end well.
If you feel you can't ignore the issue, perhaps the best thing would be to have a private conversation with the owner:
I thought the company made a profit last year, so I was surprised to hear you say it made a loss. Is there something I'm missing here?
Answers could range from "actually, it did make a loss, here's the evidence" through "none of your business" to "you're fired", so be slightly careful before asking.
If you have access to financial records/statements then I suggest you keep that on the need to know basis. Remember your obligation lies to the owner, shareholders, and government. Employees who are not cleared to know those statements or accounts are not to be included on that information without approval from the owner or shareholders (or board of directors if applicable). I would just keep quiet and depending on your position in the company, maybe talk to a higher up financial director or CFO and see if what the owner said is true. Try to throw it into a casual conversation as a per chance kind of thing (around the water cooler):
"Hey [name], I heard a rumor saying that we recorded a loss last [year/quarter/month]. How bad is it?"
The response will tell you if things are going badly or what. Be careful of asking this if you are supposed to know. Try adding a small amount of humor to lighten it.
NOTE: My answer comes with the understanding of US laws and US GAAP. Not applicable in all countries.