I'm not sure what your example represents but I don't believe many people throw up a little when they are lying or disgusted. I hear this meme on occasion from Stephanie Miller (comedian, political commentary) but to me, that simply doesn't make sense physiologically.
You might burp a bit of bile into your throat for many varied reasons, I'm not sure lying is one of them.
So back to real tells someone is lying. There are a number of disproven myths that when lying, people do certain repeatable things like put their hand to their hair. It's fine to create something like that in fiction, your character always does X when lying and the other character knows that. But research has debunked it.
On the other hand, I hear people dismiss being able to detect lies but there is some research on micro-inconsistencies being a reliable indicator of untruths. For example the person saying, "Love you too" might have a brief opposite emotion cross their face just before they smile.
5 Signs of Lying That Aren’t as Foolproof as You’d Think Discusses the myths but goes on to describe micro-expressions.
How to Detect Lies: Micro Expressions
Of course, none of this is fool-proof enough to use in a court; like lie detectors, there is an error rate. And some people believe their lies so there is always that.