I think there was WAAAAY more to it than Jodi making up some woman who allegedly came into the restaurant to tell her that Travis was dating Lisa. WAAAY more. He knew something about her and he was going to expose her because she had played too many games with him. He wouldn't have gotten that angry about her knowing about Lisa. She knew about Lisa because she followed him, hacked into his accounts, slashed their tires, and who knows what else. Did she steal some money from him? Did she do something even worse? She did SOMETHING, and he was calling her bluff on her stupid lies. He was going to tell other people what he knew about what Jodi did if she didn't come clean. She was playing him like a fiddle and, no doubt, enjoyed the drama.
Sometimes it's not WHAT a person is saying so much as HOW they are saying it. Text messages won't necessarily convey that, but Travis knew that her ostensible calmness and attempts to soothe him were only surface words that were loaded full barrel at his buttons. HE knew HOW she was saying (or NOT saying) things, without needing to hear it out loud. Her games wouldn't be as apparent to someone who didn't know BOTH of them and how they interacted with each other.