So being a math student, I've looked into this a bit and came up with the following result: the only possible way for this to happenis if damage is rounded up. It has to be, as otherwise it makes absolutely no sense. It's contradictory to other things like Speed being rounded down, but it's my only explanation. Anyway
Damage is Pokemon is calculated with a pseudo-random number generator, where it selects a value from a set of calculated number. Let's say we have a Bulky Mienfoo use U-turn on itemless Offensive Vullaby. I chose these because there are no distracting factors like STAB, type matchup, item damage modifiers, etc. This has the following rolls
(6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8)
As you can see, 3/16 rolls do 6 damage, 12/16 rolls do 7 damage, and 1/16 rolls do 8 damage. Now I have said that damage is rounding up, and I'll explain that a bit later, but let's assume that's true for now. Then it's very possible the rolls actually look quite different, maybe something like this:
(5.86, 5.92, 6.0, 6.08, 6.16, 6.24, 6.32, 6.4, 6.48, 6.56, 6.64, 6.72, 6.8, 6.9, 7.0, 7.08) (not the actual calculation, just random things I spew. I could figure out what it's supposed to be, but I don't feel like it)
If you round all of these up, you get the same rolls as above. What you see as that most of these rolls do slightly more damage than they would if you follow the damage calculation, ranging from 0.92 to 0 bonus damage out of nowhere. Of course, this is close to negligible, even in LC, since the not even 1 HP isn't very important. However, let's now look at a set of rolls for a multi-hit moves:
(3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4)
This is Shellder's Icicle Spear on itemless Bulky Mienfoo. This roll is of course for only one hit. We see 15/16 rolls do 3 damage, and 1/16 do 4 damage. As such, the calculation could look something like this:
(2.06, 2.12, 2.18, 2.24, 2.3, 2.36, 2.42, 2.48, 2.54, 2.66, 2.72, 2.78, 2.84, 2.9, 2.96, 3.02)
Once again, this matches up with the rolls that end up happening if you round everything up, and we get anywhere between 0.98 and 0.04 bonus damage. Once again, negligible, you might say. However, keep in mind this hits 5 times and you thus get anywhere between 5*0.04 = 0.2 and 5*0.98 = 4.9 bonus damage for absolutely free. That is about 5 HP of damage out of nowhere. In higher tiers, this is also negligible. But in LC, when most things have between 20 and 25 HP, that's about 25% extra damage. On average, you still get about 3 bonus damage, which is like 15% of a common health pool, which is of course incredible. This is why multi-hit moves do such an insane amount of damage in LC but nowhere else: when you round up, you get a non-negligible amount of extra damage, meaning moves that take advantage of this (multi-hit moves) are great.
So why do I say damage rounds up? Let's assume damage rounds down for a second. The Shellder's Icicle Spear could then have the following set of rolls
(3.06, 3.12, 3.18, 3.24, 3.3, 3.36, 3.42, 3.48, 3.54, 3.66, 3.72, 3.78, 3.84, 3.9, 3.96, 4.02)
As you can see, if we round down, we LOSE damage every hit,which makes no sense whatsoever if we are trying to prove it does a higher amount of damage. So in order for this to make sense, damage MUST round up. If this is wrong, this entire explanation is wrong. As a side note, the bonus damage you gain from rounding is actually a part of the reason why LC is so offensive; when your stall mons take a fairly significant amount of extra damage every turn, they can't really stall.