In a nutshell: There's more to lag than just your ping time.
Imagine that as you play LoL, every time you move, a helpful gnome scribbles something on a piece of paper and stuffs it in a manila envelope. The gnome gives the packet to a courier, who hops on a train bound for the Central Server to deliver your command.
There are two routes the courier can take. One of these routes uses an old steam locomotive. It's not very fast (taking a few days to arrive), but the tracks are pretty well maintained. It never breaks down or shows up late.
The other mode of travel is a sleek, modern maglev bullet train. It travels at 400 kph! That's fast for a train. Unfortunately, every second or third train is attacked by zombies, which derail it and eat the poor courier's brains. Also, sometimes the trains explode for no reason at all. Sadly, this is your courier's fate.
A few days later, the Central Server realizes that no couriers have shown up recently and sends a message back to you asking why you haven't sent any updates for the last week. Your helper gnome sighs dejectedly, makes another copy of your command, dispatches another courier, and hopes this packet makes it to the Central Server intact. Despite the fact that one route may be faster than another, packet loss means you can still experience overall lag.