Well, not all trades are lag-related, just a bunch of them. Things like two Rollers splatting each other at the same time makes enough sense, and the very limited speeds of ink shots means there will always be some window in which two players could get shots off before they die, and then those shots end up killing both of them. Lag between systems simply increases the size of this window by virtue of how the electrical signals are sent received, namely, opposing players receive the signals from your actions slightly later than when you did them. Essentially, other players will always see you where you were instead of where you actually are. However, this game still treats you hitting where they appear on your screen ("where they were") as if they were really there, and they will be killed accordingly. That's basically why trades in close-quarters seem to happen so often - players are continuously, and perhaps unknowingly, putting themselves into a situation that's actually very ambiguous by nature. The obvious solution to playing around this kind of lag is simply to not put yourself into that situation, i.e., make sure they're not firing at you when you're firing at them - the "golden rule of shooters" as it's said. Granted, you should be doing that anyway, but the influence of lag just means that there's less wiggle room to this concept. Kiting Rollers, for instance, is still possible with good enough movement, but it becomes harder than it should be because they can hit your "ghost" and have it work.
And fair warning, getting a better connection on your end won't save you from a bad connection on the other, or from someone who's simply very far away from you. It takes a noticeable amount of time (as in, on the scale of frames, reaching up to seconds on occasion) for these signals to go literally around the world and back to your console, as described above. That's just physics. It sucks that it can impact how the game plays, but there's nothing anyone can do to change that, you can only adapt to it.
