I've been looking for what things actually proc lich bane, and have been unsuccessful. The kinds of things I'm interested in are as follows;

Does it proc when Sion activates his shield, and again when he detonates it?
What about toggle abilities with no cooldowns like Ashe's frost shot or Sion's enrage?
Will on-hit abilities with no key activation like Teemo's toxic shot ever do it?
What about multi-shot abilities, like corki or twitch's ultimates? Will each shot proc, or only the first?
What about toggle abilities with cooldowns, like Mundo's burning rage?

Any information on these, or information about where to find information about these, would be nice, thanks.

My understanding is that it procs when first activated... secondary activations, like Sion's stun or Janna's tornado, would not set it off. (On Lux, the proc activated when you first cast your Q, not when it detonates, which is the same idea as the above 2 champs.)

So abilities like corki or Ashe where multiple shots are fired, only activate it when you first fire the shot. For toggle abilities, they are a passive and from I have seen, do not trigger the ability in any way. On hit abilities also do not proc Lich Bane, so Teemo's toxic shot or his use of Lich Bane is extremely limited at best.

http://leagueoflegends.wikia.com/wiki/Ability
http://leagueoflegends.wikia.com/wiki/Lichbane

I can't say for certain how it works, but I believe it mostly works for active abilities & activation of spells with cooldowns and rarely/never works for passives/toggles with no cooldowns. Corki's ult and Twitch's ult are quite different so I'm not sure why you lumped them together, but I'd imagine Corki's ult will proc it since you are manually firing them off one at a time. Twitch would probably proc it once on spell activation but not anymore. Doubtful you would gain another proc for 'detonating' your spell like Sion shield or Gragas barrel, but I'm not 100% sure.

Thanks for the links, but those pages don't actually answer any of the questions I had, the WIKI was one of the first places I looked.

whenever you use a non item active spell it should trigure on its initial cast. note that toggle spells arent active spells. passive spells obviously dont either.

when the spell in question is cast your champ recives a single buff which does its effect on the next auto attack you land shortly after

- It procs when Sion activates shield, not when he detonates it.
- Toggle abilities dont proc it.
- On hit abilities like Teemo's Toxic Shot won't ever do it.
- Corki's and Twich's Ultimates are completely different. With Twitch, you press R once and he shoots a lot of times, procing lich bane/tri force once. With corki u press R every time u want him to sent a missile skillshot, so it procs them each time. But remember these procs have a 2 sec cooldown.
- On the last one i am not sure, i guess it procs on activation and not on deactivation (but this need to be confirmed)