Lich king had the power to instantly kill people via snuffing out their life, he has immense psionic powers (lifting people up by their throats, telepathic communication, i could go on and on here), can freeze people solid, he can negate magic like lesser DKs can, and in order to kill him blizzard had to come up with the silly reason of "he let us lol"
Lei Shen is huge like the rest of his race, so he has great physical strength, he can wield lightning (which can be negated via null-magic zones or simple laws of energy if those are even canon in WoW)
Armies? The Lich king has got a army so vast it literally could swarm over Azeroth and kill everything... nothing short of re-origination could stop something like that
Lei Shen has construct creators, which can be destroyed if found, and if blood elves from the requliary can find them im sure Liches can find them
also most sentient mogu constructs (meaning the non-terricotta ones, ie the ones casting spells and hating everyone else) have souls, which we know are taken from mogu to be bound in stone once their body fails them or simply from birth, which could be consumed to either empower whoever consumes it, or make some sort of mogu banshee to serve the scourge
dont forget that the Lich King grows more powerful with every soul that is claimed by the scourge
(http://www.wowpedia.org/Lich_King)
i really dont see how the Lich King could lose to Lei Shen 1v1 or army vs army