❓Is it easier to get fatty liver on a vegetarian diet than an omnivorous one?

The core causes of fatty liver are chronic excess total calories, too much refined carbs and added sugar, and lack of exercise — it has little to do with the label of "eating meat or not," and much more to do with what specific types of food you're eating. There is a real "pseudo-vegetarian trap" though: some people, after switching to vegetarian, end up relying heavily on refined carbs, fried vegetarian foods (fried tofu, fried rice cakes), sugary drinks, and desserts to feel satisfied. That kind of eating pattern can have higher calorie and refined sugar content than a normal balanced diet with meat, and over the long term it really can increase fatty liver risk, but that's a case of an unbalanced diet, and the root cause is eating the wrong things, not eating vegetarian. Conversely, a well-planned vegetarian pattern centered on whole grains, legumes, and vegetables is actually associated with lower rates of non-alcoholic fatty liver disease in multiple studies. The real standard for judgment still comes down to what you're specifically eating, and whether your total calories and added sugar are reasonable, not simply predicting fatty liver risk based on "vegetarian vs. meat-eater."