If things still don't make sense, worry not. This is going to be one of those comics with a very watery plot that fills in the gaps later on.
In this page, it's established that the world of waiters is a free-for-all competition that has its share of allies and grudges. Here, our narrator and another Waiter "Lawrence" have crossed paths on some less-than-friendly terms.
More to come. Don't expect anything this week, though.