Was your sister flying with you at the same time? Or was she flying on a different date but just the same routing?

I'd say it's a coincidence. Which doesn't necessarily mean it wasn't the same or similar cause. But if there were a systemic problem with something consistently afoul every single time on a certain route, then you likely would have gotten sick more often. And there probably would have been some publicized incidents with multiple travelers from a flight getting sick.

I wouldn't automatically assume it's the LAX-ITO leg. Symptoms like that can take anywhere from a few hours to a few days to develop, depending on the organism causing it. So it could have been acquired...at home before departure...at LHR...on the LHR-LAX leg...on the last leg...after arrival at ITO. It could be contamination you touched and then contacted your mouth or nose; contaminated food; an unknown food allergy; an airborne culprit.

To narrow down what might be the differentiating factor(s), you would need to carefully list and compare - as much as you can remember - what you did and consumed on the "sick" trips and one or more of the "healthy" trips, and analyze it. Even then you won't be able to pinpoint random incidents (e.g., transferring bacteria from a visually clean but contaminated surface to your body). But you might have some ideas.

Good luck, hope you stay well next trip!