How else would they have made Mon-El's anti-lead serum?
Ooooh, good point!
It was established in LSH stories that Mon-El's anti-lead serum had, as one of its principal ingredients, powdered Kryptonite. This would explain why they would keep that sort of stuff around.
Kryptonite, for one thing, seems to be much more common in the 30th Century than it is in the 20th. For one thing, in the first appearance of Shadow Lass (at least chronologically, anyway) the warlords on Talok were shown to have stockpiled Kryptonite, presumably because they anticipated the involvement of Superboy. Showing that if you're a self-respecting would-be dictator, it's logical to have an anti-Superboy defense.
Only a few issues prior, the entire EARTH was covered with a shower of K-dust. The ENTIRE EARTH. I mean, that's a lot of Kryptonite.
LSH enemies used Kryptonite a lot more than Superman's foes in the regular comic did; for instance, witness the laser beams equipped to fire Green Kryptonite that were used in the citadel of the Dark Man/Tharok, or the Emerald Empress's Kryptonite handfuls.
There can be several explanations for this:
1) As Superboy's existence, secret identity, and weaknesses are "history," his enemies in that era would know about them more commonly than his foes in the 20th;
2) Because of the higher technological level of the 30th Century, it may be easier to create "artificial Kryptonite;"
3) Kryptonite that went to other worlds can be found and used in an era where space travel is commonplace.
One of the more interesting (though less consistently handled) weaknesses that Superman has is magic.
There was a very cool explanation for why Superman was vulnerable to magic, which was that the use of sorcery and magic is incredibly rare among Kryptonians, and since none of Superman's ancestors were magicians, he has a genetic vulnerability to magical effects, just like those with a genetic problem with albinism are vulnerable to sunburn and skin cancer.
As most earth people have a greater history with magic in their ancestry, almost no Earth people show a similar vulnerability.
(The implications of this are neat to think about: if you're Irish-American, maybe the reason you're not vulnerable to magic the way Superman is, is because you've got a Leprechaun in your family tree 20 generations back or thereabouts!)